[bestcellar]

I don't see an opponent raising a jack on the flop. I'm not sure whether three betting will drive him away though, so calling may have been the right play.

on the turn, you are almost certainly ahead. Check calling is fine again because if you reverse or check/raise you might scare villain away.

On the river, I would lead out for value. If you do get popped, you will know you are probably facing a jack played really well, or possibly a straight, but any call is $$$$ in the bank. A check allows him to check behind too much, as he did.