Im not sure I can help but I think we should look at the possibility of our Thweatts being from the same line.
My great great great great grandfather was Arthur F. Thweatt who moved to Polk county arkansas between 1860 and 1874.He is widowed in 1900 at age 74 and living with his son James.His son Gerome lives next door.A.F. Thweatt you have listed may have a death certificate and possibly link him to one of Arthurs grandchildren.
My great great grandmother was Medora Indhendant Hampton and is in Arthur Thweatts 1880 Polk County Arkansas home listed as granddaughter age 6.Her mother was Mary Thweatt, I dont know what happened to Mary Thweatt, I assume she died as Medora was raised by her maternal side the Thweatts.Medora's death certificate list her mother as Mary Thweatt.
Anyway I have the Arthur Thweatt family in 1850 1860 1880 and 1900 census, I am unsure if your A.F. relates, however I only know of one Thweatt family in Polk county Ark.
I have went on email me at firstname.lastname@example.org and I can provide these records and maybe we can connect A.F.