source: NJ Colonial Documents, West Jersey Records, Liber B, part 2 p732 Deed 13 Mar 1702/3. Thomas Branson, husbandman, to Thomas Ridgway, yeoman, both of Springfield township, Burlington Co, for 100 acres there.
source: NJ Archives: Thos Branson with Michael Newbould, Thos Douglasse inventoried the estate of Wm Mills of Springfield, Burlington Co, yeoman, 16 Nov 1714. (personal estate = L39.2.4) Recheck this: were 2 TBs involved?
source: NJ Wills. 10 May 1731, Thos Lewis of Hanover, Burlington Co, Schoolmaster. Died intestate. Inventory notes debts due from: THOS BRANSON, Wm Rogers Jr, Jos Rogers, Dr. Wright, Steven Wright, ten others. So he must have been sending some kid(s) to school; the timing would be right.
source: NJ Wills. 15 Jan 1731/2 will, John Scholey of Springfield, Burlington, yeoman, mentions "meadow adj Thos Branson."
source: VA Patents 16 p385: 12 Nov 1735: Thomas Branson 850 ac beginning at Jost Hite's; head of the south branch of the Opeckon.
Lord Fairfax visited Thomas Sr's home in Warren Co VA in 1734 (p 1586, court records of the Lord Fairfax land suit). "John Dyer...deposeth and saith that many years ago when Lord Fairfax entered a Caveat in the Secretary's office against granting lands to the Westward of the Blue Ridge, his Lordship came over the ledge of mountains to visit the country on this side of the Blue Ridge to the house of one Thomas Branson. That some time after his Lordship came into the house, Branson made application to his Lordship to know in what manner people should act to secure their Rights, and that he made answer it would make no difference, that it would only be changing of landlords, paying the Quitrents to him instead of the King in case that he would succeed in his suit and that he wanted to have the Country settled and further that he would not hvae any poor man quit the place for want of land and upon being asked by Branson how Mr. Hite would come off, who had an order of Council for a very large tract of land, his Lordship made answer that he would be very well, for he was desirous of having the Land settled and further the Deponent saith not." This statement was made in 1762.
Will probated NJ and VA New Jersey Colonial Documents, Calendar of Wills 1730-1750 p 58 lists children.
You can find the History of Burlington and Mercer Counties, New Jersey with biographical sketches of many of their pioneers and prominent men online at hathitrust available to read or download for free, or look for a hardback copy at Amazon.