Mr. Caylor,
My research fails to suggest a connection between the Caylors of Washington Co., VA and those Caylors who lived in Blount County, TN; my research also fails to disprove a connection. Not much can be proved regarding the parentage of the earliest Blount Caylor [George, born about 1775] or even his location prior to 1800. So his relationship to other Caylors in the US remains largely unknown.
However....
Have you done a y-DNA test?
If you'd like to do a direct comparison of your y-DNA test results to those of someone verified as belonging to the line of George Caylor, Sr. of Blount County, TN, go read the message at
http://genforum.genealogy.com/caylor/messages/517.html
to see how to find that descendant's test results [that George Caylor descendant tested his y chromosome DNA through FamilyTreeDNA.com at the 37 marker level in 2011; another distant Caylor cousin - also of the George Caylor, Sr. lineage though via a different son - recently compared markers and matched for the 12 markers he tested.]