Thomas Waite's children and further descendants etc. are listed in this NEHG's edition viewable online. You could start tracing from there. See: Pages 292- 305
(p. 292) THOMAS WAITE of Portsmouth RI husbandman born probably in England about 1615 died shortly before 14 Dec 1669 He married Eleanor ___.
The New England Historical and Genealogical Register Vols. 37-52 (1883-98) include section: Genealogical gleanings in England, by H. F. Waters., 1919
Maine, Vital Records
Citing this Record: "Maine, Vital Records, 1670-1907 ", index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/2HK3-H8G), James Swellage Waite, 1811.
Name: James Swellage Waite
Birth Male 16 Sep 1811 Portland, , Maine, United States
Father: John Waite
Mother: Sally N
Maine, Nathan Hale Cemetery Collection, ca. 1780-1980
Name: John Waite
Burial 1838 Portland, Cumberland, Maine
Age: 87 Birth (Estimated): 1751
Death Date: 16 Mar 1838
Spouse: Sally N. Died Feb. 3, 1853 age 80
There are user submitted pedigrees - which would require further confirmation/sources - for John Wait and Sally - indicating John's parents are Benjamin Wait and Abigail Isley.