Michael,
 
I found additional evidence that seems to link Thadeus and Abraham Cooley. 
 
A book on civil war includes letters from a private John T Cooley writing to his cousin Julia Ann (Cooley) Price in 1864.  Julia Ann Cooley Price was the daughter of Benjamin F Cooley, Abraham's son.  Pvt John T Cooley was the son of John Tucker Cooley Sr, who was the son of Daniel Cooley, son of Thadeus (listed as Tucker Cooley, son of Daniel in Thadeus' 1814 will).  I found another posting indicating Daniel's children were John Tucker and Sally Cooley (below), which also supports John Tucker as son of Daniel. John Tucker Sr. lived his life in Wythe and Tazewell Counties, near to descendents of Thadeus.  Abraham and his children lived in Grayson and Carroll Counties. 
 
Given this info, the letters seem to provide strong evidence that Thadeus and Abraham were brothers.  
 
Regards
 
John
 
http://books.google.pl/books?id=cRSWZug8YowC&printsec=frontcover&dq=Why+Confederates+fought+:+family+and+nation+in+Civil+War+Virginia&hl=en&sa=X&ei=Q5ctT6TWBobFswbE_5DtDA&redir_esc=y#v=snippet&q=john%20t%20cooley&f=false  
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2. DAVID2 COLLINS (DAVID1) was born Abt. 1787 in Montgomery Co., Va., and died March 1866 in Wythe Co., Va. He married ELIZABETH STEPHENS Bef. 1815.

Notes for DAVID COLLINS:Listed in Wythe Co. census records 1820/30/40/50/60 1831 Mar 15: David and Elizabeth sold land in Montgomery Co., Stoney Creek on Main Rd. 1832 Mar 6: David and Elizabeth sold land in Montgomery Co. (formerly owned by David Collins)

Notes for ELIZABETH STEPHENS: She was the widow of Daniel Cooley (son of Thaddeus Cooley) and mother of 2 children, John Tucker and Sally Cooley) when she married David Collins.

http://familytreemaker.genealogy.com/users/l/u/n/Susan-Lundy/GENE7-0002.html