As is typical in most secondary sources, no explanation is given how it is determined which John was the son of Jacob. Neither couple appears to have named a child either Jacob or Abigail. There is reason to doubt Hodgman's pairing: *Since the John who married Mary Kendall died in Tyngsboro in 1816, in his 93rd year, he is of the right age to be the son of Jacob and Abigail, (but there is a John Wright of Charlestown of the same age so we cannot simply jump to this conclusion). *Since the John who married Sarah moved to Dunstable, and since a John Wright died in Dunstable 1802, aged 68, i.e., too young to marry Mary Kendall but just right for marrying Sarah, the husband of Sarah may not be born in 1723, but a decade later.
Given the commonness of the name John Wright, it is impossible with this limited evidence to credibly identify which of these two, or possibly another, is the son of Jacob and Abigail.