There was a John Hawks living in Hingham, Norfolk, England when sons were baptized in 1602 and 1605. On 27 Jan 1612, a John Hawks there married Mary Cowper. A daughter of John was baptized at St. James in Norwich on 3 Sep 1626, and a son Nicholas bpt 21 Dec 1628. A John Hawks died 20 July 1628, and Nicholas Hawks d. 14 May 1629. Since Adam Hawks came on the same ship as John, it would seem that they were either brothers or father and son. Ages make more sense if they are brothers, children of John who married Mary Cowper as a second wife and died in 1628.
Marriage 1 Mary COWPER b: ABT 1575