I wonder if this Abner is the Absolem/Abner Davidson of Prince Edward VA. The latter disappears from PE by 1820. He only reports 1 son in the 1810 census, but it would not be surprising if Jesse's age was reported wrong.

Abner Davidson married Peggy Blanton about 21 Dec 1803.

There was an Abner Davidson in the 1820 census of Northumberland VA. However, it is near Chesapeake Bay, an unlikely migration from PE.