You're in about the same spot I am... Thomas White (but I really don't think he's a Jr.) married Huldah Gurney, 2 January 1803 in Freetown, Bristol, MA. Children:
Peregrine, Jan. 4, 1804.
Silus Gurney, Feb. 1, 1806. (aka Silas)
James Harva, Apr. 29, 1807.
Thomas Howland, May 26, 1810.
Rolun Palmer, Sept. 16, 1812.
Nicholas Hathaway, July 27, 1814.
Bibliographic Information: Vital Records of Dartmouth, Massachusetts to the year 1850 volume I-Births. New England Historic Genealogical Society. Boston. 1930. Call Number: F74.D25D23 vol.1, pp 296/7.
PUBLISHED BY THE NEW ENGLAND HISTORIC GENEALOGICAL SOCIETY AT THE ROBERT HENRY EDDY MEMORIAL ROOMS AT THE CHARGE OF THE EDDY TOWN-RECORD FUND BOSTON, MASS. 1929.
I am currently working on a theory that Thomas' father was Peregrine White of Freetown, MA who married Mary Howland, daughter of Malachi Howland and Hope Dwelly, of Middleborough on May 3, 1770, and had children: 1) Thomas; 2) Malachi, b. 7 Oct 1785, Freetown; 3) Hope. I am working on this theory because of the family's use of surnames as middle names.
I'll let you know if I find out any more!!!