After checking behind, Villain has to expect you to bet the river even if you have air, so there's a good chance you'll get paid off here. If I'm subtracting right, Villain's got about 60K left, so probably in the neighborhood of 25-30K is an amount he'll be willing to look you up for if he's got a pair.

If you bet 25K and he moves in, well, I think I'd fold, but maybe I'm weak tight. I just can't see him doing that without AQ. Even with a lower set, I think he'd just call you (I also think he doesn't check the turn with a set).

I don't like check calling to induce a bluff, I think he probably has a hand that he wants to show down cheap and will check behind a lot of hands that he'd pay off a bet with.