There were several John Williams families in Carter Co. at the time period you mention. This may be a long shot but there was a John Williams age 30-40 on the 1840 Johnson Co Census with a wife age 30-40, 1 f child 5 or less and 1m child 5 or less. Living close by were several Reece families -Hugh, age 20-30; Jacob age 60-70; John Jr age 30-40. Also living near is a William S. Williams, age 50-60-no wife of the same age .John Williams does not appear in 1850. The other families that do appear include William S. Williams age 64, b. in NC; Hugh Reece Jr , 33,b. NC, Hugh Reece, 40, b. TN; John Reece,40, b. NC. In 1860, all of these families are living in the Trade, TN area (near the NC line). William S. Williams is living with the William and Mary Greer family. (Perhaps a marriage connection?)William is 70 and wife Elizabeth is 52(both b. in NC). Have you found any Greer connections in your tree? The Greers were from Ashe, NC. but trace back to Baltimore Co. , MD. Living next to the Williams and Greers was Benjamin Greer and wife Elizabeth Reece Greer (b. 1808 NC). These surnames seem to be connected to yours. Sometimes it helps to track families close by when you get stuck if you have no other references to go by. Good luck in your search.