I would most certainly take a bet/check/bet line here, he prob has enough showdownvalue w a couple of Jx or pairs up to TT. He's checking back all those otr expecting to be good a decent % of the time. I dont think there are any FD's in his range that check behind on the turn especially when an ace peels, becomes a fairly easy bet/bet line for him then, not to mention Ax/KQs floats. I think the rest of his range is heavily weighted on pairs and Jx combos that have enough sd value to x behind, esp when it looks like u entirely gave up on the hand, and will fold out only worse by betting himself.

So yes, you can bet here for value.

Thanks for your reply Cairy. I think that you are spot on, that if he had had an ace he would have bet turn, to make me pay jacks and draws, so I had place to bet river. Thank you!

I like a turn bet here.  The A is a card that you are going to use to fire at when you have air, you keep control while your OOP and you get value from his draws.  There is a good chance he isnt folding a J either at this point.  Given the check through I like betting the river for the reasons given above.