Elizabeth's parentage is stated wrongly in many references available on the Internet.

Based upon my research I feel fairly certain that she is the daughter of Robert & Catherine (Kilham). Some sources on the Internet have her born much later, to Robert's 2nd wife, and such data would make Elizabeth 11 years old at the birth of her 3rd child, Sarah Smith, on October 20, 1660.

Elizabeth married John Smith, had 5 children by him, then married William Bennett and had one daughter, Grace.

At the time of her father's death in 1682 he names only his daughter Elizabeth Bennett (last name from her second marriage) and her son John Smith. (Her father had already provided for his other children via gifts during his lifetime.)

From "The Ancestry of Lydia Harmon 1755-1836":
iv. ELIZABETH. She m. John Smith of Salem Village. It seems probable that after their marriage they lived with her father, Smith helping in the management of the farm. The evidence in the case against him and his sister-in-law, the wife of Zachariah Goodale, in 1672, would seem to indicate that the marriage was not a particularly happy one. Smith d. before March, 1674/5, when Elizabeth m. William Bennett of Salem. As her father states in his will, he and her stepmother lived with this daughter until his death. She was a widow in 1692, living with her son Abraham.

Children:--

1. John Smith. He m. Ann Skerry, Feb. 6, 1689. He was a maltster (brewer) in Salem in 1692.
2. Mary Smith. She m. Mark Haskell of Beverly, carpenter, March 20, 1677/8.
3. Sarah Smith, b. Oct. 20, 1660; m. John Clark of Beverly, weaver.
4. Elizabeth Smith, b. June 5, 1662; m. Humphrey Horrill of Beverly, Jan. 10, 1687/8.
5. Abraham Smith. By deed and release from his brother and sisters he acquired the Goodale homestead, which had been left by his grandfather to his mother, and also the property deeded to her in 1678. He conveyed the estate to his son Nathan in 1740. (Essex County Deeds 80: 75.)
6. Grace Bennett, b. Feb. 1676; d. young.

• Married: BEF 1658 in Salem, Essex Co., Massachusetts
• Note:

  From "Descendants of John Hewes" (genealogylibrary.com):
  SMITH FAMILY
  JOHN SMITH of Salem married ELIZABETH GOODALE, daughter of Robert Goodale, before 1658, as on that date he calls Robert Goodale his father-in-law (Essex Deeds, Vol. I, p. 40). She was baptized at First Church, probably 31-3 mo-1640. An inventory of the estate of John Smith was returned by widow Elizabeth, 16-5 mo., 1672. She married, second, March, 1674-5, William Bennett.
  
  Children:
  
  ABRAHAM, born probably about 1658, baptized 28 Aug., 1670.
  JOHN, baptized 28 Aug., 1670.
  SARAH, baptized 28 Aug., 1670.
  MARY, baptized 28 Aug., 1670.
  ELIZABETH, baptized 28 Aug., 1670.
  ELIZABETH, baptized 8 Aug., 1672.
  
  Contradicting information: John Smith had not yet married Elizabeth Goodale when he purchased land from Elizabeth's father Robert in 1658. (Research of Jana Ulrich: http://hometown.aol.com/janau/index.htm)
  
  Note regarding the text below: Make note of the participation of Giles and (second wife) Mary Corey in the court cases. Giles was pressed to death as a witch in 1692, partially for having beaten to death Jacob Goodale, the brother of Elizabeth and Zachariah. (Giles' third wife Martha was hanged as a witch 3 days later.) As you will see, it was Giles and one other man who spared John Smith from his whipping and fines in 1672. (See http://www.mayflowerfamilies.com/)
  
  In 1676 Dr. Zerubbabel Endecott was a member of a jury which held inquest on the body of Jacob Goodale, servant of Giles Corey (and brother of Elizabeth Goodale Smith), after his sudden death. It appeared that the man was "almost a Natural Fool." The body was badly bruised and Dr. Endecott performed a post mortem, finding "clodders of Blood" about the heart. Despite this finding, Giles Corey was never convicted of causing the death. (Dr. Endecott was the son of Governor John Endicott, who was fined for striking another of my ancestors, the irascible Thomas Dexter.) ("The Ancestors of Charles Clement Heacock", genealogylibrary.com.)
  
  Seventeen years later Ann Putnam cried out against Giles, saying that the ghost of Jacob appeared to her in his winding sheets, claiming that Corey had escaped a trial and death by making a pact with the devil. (http://etext.virginia.edu/salem/witchcraft/texts/ , Narratives of the Witchcraft Cases by George Lincoln Burr, from "The Wonders of the Invisible World," by Cotton Mather, 1693.)
  
  Also from the Research of Jana Ulrich:
  
  A juicy little "scandal" involving Zechariah's wife, Elizabeth and his sister Elizabeth's husband, John Smith must have kept the gossips armed for a while. Apparently, brother John couldn't keep his hands to himself and had quite an eye for the ladies. Elizabeth let slip to a few of her friends that brother John had made some inappropriate advances to her and, then as now, apparently, a secret has no value unless shared! When brother John learned through the grapevine that his sister-in-law was saying less than complimentary things about him, he sued her for slander in the Salem Quarterly Court of 1672. One of the Goodell's defenses was that slandering brother John wouldn't be easy! From the looks of the court records, the whole neighborhood got involved and Smith was found guilty of a countercharge filed by Elizabeth Goodell. He was fined and sentenced to be whipped, though this latter punishment was remitted when his friends promised to pay his fines. Synopsis of the court records follow:
  
  June: John Smith v. Zachariah Goodell and Elizabeth, his wife. Slander. The defendant allowed costs.
  
  Writ, dated June 10, 1672, signed by Hilliard Veren, for the court, and no return made. Bond of Zachariah (his mark) Goodell and Elzabeth (her mark) Goodel.
  Bill of cost, 7s, 6d.
  
  Plaintiff's plea: that he objects to defendant saying that she kept the abuses, which he was alleged to have committed, private for years and would never have revealed them but to save herself from damage against her in court.
  
  "Now if a woman might singly alone be so surcomstansed noe man can scap from suffering: but if I might be sufred to sware in my owne case I can safly sware that her charg and accusation is fals but let the considaration of the testamony the Nayborhowd that will say that thay neuer saw any hurt by me in that respect but do raly thinke that I am wronged and I hope that I neuer shall be left to Committ shuch wickedness pray haue soe much charity towards me as to credit me in what I say: now I hop that no man can according to law be condemned without it be by the mouth of tow or thre wittnissis and in this case wher ther is noe surcomstanc in the Case to Joyne with her complynt thus hoping to confidently believe as raly I dow that my grettest hapynes lyeth in that your worships are holly wiss and just and charitable."
  
  Defendant's plea: the court was asked to judge of the legality of the attachment, for the law provides six days for the defendant to prepare his answer and testimony; the attachment was for slander but mentions no time nor place nor word of slander; defendant had said many things concerning plaintiff for many years upon many occasions and if common fame my be credited "it is not a very easy matter to slander the plaintiff." Summons appearing not to be legal, defendant requested a nonsuit.
  
  John Smith and Elizabeth, wife of Zachariah Goodell, being bound over to this court to answer to several abusive and uncivil carriages between them, with which said Elizabeth charged said Smith, the latter desired to be tried by a jury, who found him guilty. Court ordered him to be whipped on the next lecture day in Salem and to remain in prison until the sentence be executed unless he pay 40s. Upon supplication of Anthony Needham and Giles Coree, who engaged to pay the fine and gaol charges within two months, his sentence of being whipped was remitted.
  
  Summons to constable, John Suthwick of Salem, for the apprehension of John Smith, and Elizabeth, wife of Zachery Goodell, and to bring them to Mr. John Gardner's, dated 11: 4: 1672 (4 Jun 1672). Summons also for witness, Gould and his wife, Tho. Flynt's wife, Coree's wife, Carrill's wife, Anne Needham and Kelam's wife, dated 15:4:1672 (15 Jun 1672), and signed by Wm. Hathorne, assistant.
  
  Lot Killum and Zacheriah Goodell deposed that John Smith, being at said Goodell's house, the latter's wife being present, said that he was sorry for what he had done to Goodell's wife and prayed God to give him repentance, hoping he should do so no more. Zacheriah replied that he wished God would give him repentance.
  
  Edward Beachum and Zachariah Goodell were bound for the latter's wife Elizabeth's appearance. Thomas Flint, Giles Coree, John Rubton and John Smith were bound for Smith's appearance.
  
  John Tomkins, sr., John Small and his wife, John Foster and his wife, John Pease, George Jacobs and his wife, Eliz. Symonds, sr., James Symonds and his wife and john Tompkins, jr., certified that they "being nere neighbores unto Elizabeth Goodel, the daughter of Edw Beachom and having had acquaintance with her from her childhood to her marriage Do testify yt according to our best observation and judgment shee hath been of an honist civill conversation & one yt would not wrong the truth in her speches."
  
  Mary Corey, aged about forty-three years, and Mary Carrill, aged about thirty-five years, testified that Elizabeth Goodell told them that one time as John Smith, her brother-in-law, was working in a swamp near her house, he called to her for fire, so she carried it to him and laid it on the side of the brook, he being on the other side. He asked her to tarry and smoke, and she told him she had already smoked, so she ran away up the hill and he ran after her, etc. Also at another time he assaulted her when he fetched her from her house to help his wife when she lay in, so that she jumped from the horse on which they rode. Also when he was at Lott Keellam's digging a well, and once on a Lord's day while her husband was at meeting, etc. She said he was an ugly rogue and threatened to tell her husband, and that he had been uncivil to her ever since her son Zachery was a little boy, but she feared that if she told her husband, said Smith would kill her or her children or hurt her creatures. She told deponents that these things were true and that she would swear to them before the best magistrate in New England.
  
  Hannah Flint, aged about twenty-two years, deposed that she was at John Smith's house at the time of his wife's lying in, and Elizabeth, wife of Zachary Goodell was there also, etc. Deponent heard said Elizabeth tell of lascivious language used by both herself and Smith, and also heard Patience, wife of Isacke Goodell, affirm to her sister's face, etc.
  
  Patience Goodell and Hanah Kellum testified that the foolish words that their sister Elizabeth Goodell spoke to them about Smith were said in a jesting way.
  
  Zachary Goodel declared to the court on his wife's behalf that "he hath not found his wives affections in ye least alienated from him, but she doth love and respect his as well if not better since these things between John Smith & her have bin reported, from ye time of ye first therof unto this time as ever she did before."
  
  Geyles Corey, aged about fifty-five years, deposed that Elizabeth, wife of Zackary Goodell, related to him that on a morning after she and his wife had been at the house of Nathaniel Carrell, coming into deponent's house, John Smith being there, said Elizabeth had been affronted by said Smith. Deponent asked her where he and his wife and daughters were. Her answer was that she was in the house and went up the ladder into the chamber and that his wife was near some bushes at the door taking in linen. He said if there had been anything amiss, she should have told him then, but when he came down he saw nothing but laughing and smoking. Elizabeth said that she was like to have broken her brother Smith's head with the ladle and his wife said if she had, there would have been but six pence or a groat to pay. Later Elizabeth told deponent that she knew he was in the house, etc.
  
  Lott Killum deposed that his wife being lame from a fall that she received upon a rock, John Smith offered her abuse, and she told him of it at night. Whereupon deponent dealt with said Smith privately about it.
  
  An Needham deposed that she and her husband were in Elizabeth Goodell's house, with the wife of Thomas Flint, when deponent's husband told said Elizabeth that she was foolish to have reported such stories, and she said that they would not have gotten out if she could have helped it. Also that deponent heard Nethanel Carall say that Elizabeth had said several times in his house this winter that she wished that the old folks were gone, etc. Also that the wife of Robbert Goodell told Hanna Flinte that in the winter time she told her old man that Smith and Betty were together very much.
  
  John Harrod and his wife testified to the same.
  
  The answer of Elizabeth, wife of Zach. Goodell: that the stories had been grossly exaggerated; that she had told what had happened to her husband and her sister Hannah Killum in private, but it had "come to the mouths of such talkers as have pverted the truth and made the matter appere far worse then euer it was to my great Scandall and reproach. Mary Gory & Mary Carril hearing of it came to enquire of me how it was, and I foolishly told my ptended friends what before I had told my Sister Killum; "That the reason she did not complain to the authority was because she was afraid Smith would do her harm, as she was often alone with her children and remote from neighbors; that if she had complained and he had been punished, "what a sad life should I have had with my Husbands relations, Again I hoped he would reforme & being a relation I thought a privet healing might make it up, and I was some advised when it was known, not to complaine against him because it would as they thought ruin his family, he being desperate some times, I was resolved to complaine against him as Mary Gory & Mary Carril do witness I told John Smith I would & to that end did go downe the towne to acquaint Majr Hathorne with it but was discouraged by others and being foolish & not acquainted with the Law did forbear untill the Major was to go to the Generl Court and when he came home againe I pceiued that it was so spread abrode through indiscretion" etc. that she was heartily sorry for her foolish words and "I desire to be humbled that I sould any way be an occasion of filling the mouths of any with pfane and sinful words to ye Dishonor of the Great God and the scandal of the Gospell ... And I desire it may be warning to mee & to us all never more to jest or speake foolishly vainly or slitely of such matters as should be cloathed with gravity & modesty, and I do acknowledge tis a dishonor to ye Sect of women ... but this I can truly say ... I love my husband as dearly as ever I did and no man else with such a love and I thinke he will say that he neuer saw cause from mee to thinke the contrary ... I desire that the truth should not be wronged nor yet that John Smith should suffer more then he heth deserved ... I thinke my neighbours amongst whome I have lived in the north field can testifie that they never saw any uncivill cariage by mee from my Childhood untill I was married. The language John Smith used to me and the Actions were such as most tend to ye way of his calling in dealing wth Cattel and not so like unlawfull dalliances tending to uncleanness."

1. John Smith II b: BEF 1658 in Salem, Essex Co., Massachusetts
2. Mary Smith b: 1658 in Salem, Essex Co., Massachusetts
3. Sarah Smith b: 20 OCT 1660 in Salem, Essex Co., Massachusetts
4. Elizabeth Smith b: 5 JUN 1662 in Salem, Essex Co., Massachusetts
5. Abraham Smith b: ABT 1667 in Salem, Essex Co., Massachusetts
6. Elizabeth Smith b: 6 JAN 1670/71 in Salem, Essex Co., Massachusetts

• Married: MAR 1674/75 in Salem, Essex Co., Massachusetts ⁴

1. Grace Bennett b: FEB 1675/76 in Salem, Essex Co., Massachusetts

1. Title: LDS Ancestral File (R)
   Author: The Church of Jesus Christ of Latter-day Saints, familysearch.com
   Repository:
   Note:
   NAME Family History Library
   ADDR 35 N West Temple Street
   CONT Salt Lake City, UT 84150 USA
   Media: Electronic
2. Title: TAG, The American Genealogist
   Repository:
   Media: Magazine
   Page: 43: 19-26
3. Title: See notes for the father
   Repository:
   Media: Other
4. Title: Ancestry of Lydia Harmon 1755-1836
   Author: Walter Goodwin Davis
   Publication: available at genealogylibrary.com
   Repository:
   Media: Book
5. Title: Calculated from siblings' or parents' dates
   Repository:
   Media: Other
   Text: mentioned in her father's will in 1682