For you western PA Axtons, here is a little clue that may be useful:
"Axton, Jeremiah, Grafton, Va., Feb. 10, ae. 85, was born in the eastern part of Va., and at an early day emigrated to Western Pennsylvania, where he resided about 50 years. He served in the army commanded by Gen. Harrison, in the last war with Great Britain. Mr. Axton was a plain, industrious, upright man, and a good citizen."
Annual Obituary Notices of Eminent Persons Who Have Died in the United States for 1857, by Hon. Nathan Crosby; Phillips, Sampson and Company, Boston, 1858