I might consider leading the turn. If he has the courage to move in after you lead at the flop and turn; I'd give him more credit for a hand. The way the hand played out; I think it's a tough decision, but I'd lean towards folding.
Reasons for folding:
1) He limped in then pumped it up on a Jxx board; what hands would he open limp that would contain a J? Seems more like a set or a slowplayed big pair that didn't like the drawy board. On the turn, both a J or a big pair don't make sense anymore with the ace on board.
2) Stacks are pretty deep; and you don't have much invested.
Reasons for calling:
1) The overbet. As Miffed22001 mentioned; it screams bluff/semi-bluff. Then again I know of players that would move in with a set in this spot; either hoping that you had the nut flush draw and won't fold your top pair; or that you would think they were bluffing and call with a J/A.