A very basic outline of what I can reasonably prove:
My 4g-grandparents William Roberts and Ann Vandergriff married in 1784 Wilkes Co, NC. Both born in the Raleigh area and may have known each other as children. Followed her family west through eastern Tennessee. No other TN Roberts family clearly connected, though a Reuben Roberts and a few others are suspect.
In 1832, William Roberts filed his Revolutionary War pension application (#S17054) while living in Hamilton Co, TN near what is now Chattanooga. In 1836, William's soon Jacob purchased land on Walden's Ridge, soon followed by Ninion Roberts who Jacob was a witness.
Look at the 1840 census for District 2, Hamilton Co, TN. The first "H" Roberts is actually Ninion Roberts, who I am 99% sure is a son of William and Ann. In 1847, Ninion and his son Emerson bought land for a mill in the same area. If you look at a current map just outside Chattanooga in the Falling Water area is a Roberts Mill Road, and hidden on the hill above foundation for the mill is the Roberts Cemetery.
The first William Roberts are my 3g-grandparents William A. Roberts/Robbirds and Jane Bunch. Their oldest child is my 2g-grandfather William Mattison Roberts/Robbirds/Robirds.
Next is Jacob Roberts. Listed next to him is David Bunch. David is Jane's older brother, and his first wife was Jacob Roberts' daughter Lucy. Next to David Bunch is a Joseph Roberts.
The "C" and second William Roberts are Jacob's sons Caswell and William G. And of course, they are surrounded by their Vandergriff relatives. In 1842, the elder William with sons William M. and Jacob, plus their extended families (except two of Jacob's married daughters) moved to SW Missouri. Ninion and his line stayed in the area.
At this point I do not know who Joseph Roberts is, but I do have information that makes him a suspect. Referring to William Roberts' pension application shows it was witnessed by Gilbert Vandergriff (his brother in law) and John Howeth. The Howeth family had been neighbors of the Roberts and Vandergriffs much earlier in Grainger Co, TN. The Howeths moved to Hamilton Co. much earlier some apparently by 1817 and are listed in the 1830 and 1840 census. The 1846 Voter List for the Republic of Texas shows David Bunch, various Howeths and your Joseph Roberts all in Rusk County. John Howeth and David Bunch are found in Grayson Co, TX by 1852, though John and his brother Thomas with much of their family soon moved just west to Gainesville in Cooke Co. Without a doubt, David Bunch is somehow related to the Howeths perhaps as close as a brother-in-law or half-brother.
Various records support that everyone knew each other in Rusk Co. and had land in the same corner of the county. The Birdwell family was apparently also out of Hamilton Co, TN, and maybe even earlier out of Grainger Co. There was an issue where George Birdwell was the exector of Robert Bell's estate, but after George died William Howeth petitioned the court to be named as executor but Matthew Birdwell protested. William Howeth had married a Bell, so Robert Bell was apparently his father-in-law.
I have looked at others research on Joseph Roberts, and think it is unusual that he just shows up in Texas and no one seems to say from where. If it is the same Joseph Roberts as 1840 Hamilton Co, then he should have some older children from an earlier marriage that is never mentioned. David Bunch did later sell some of his land in Grayson Co. to a Roberts, but I can't get anywhere with that.
I won't claim for sure that Joseph Roberts is related to my Roberts, but I think the Bunch/Howeth connection suggests the clear possibility due to various "coincidences". Do you have a male Roberts cousin that might be willing to particiapte in the Roberts Y-DNA project. There is another Roberts family not related by blood long associated with the Bunch family that was in the same area of Tennessee, so there is a chance that the 1840 Joseph Roberts is connected to them through David Bunch.