Hmm...check or push. I'm leaning towards checking turn and calling a river bet or value betting if it's checked to you.

Tough though because he's probably calling a push with any jack or 10. But right now you don't know you have the best hand, while if he checks the river to you, then you probably do especially if you show signs of slowing down by checking the turn. But bleh, lots of draws up there now. I dunno