How to play this river? ($10+1 Party, ITM)

[Ixnert]

About 3.5 hours into a $10+1 at Party, blinds 2500/5K. 53 or so players remain of 2500-some to start, so we're well into the money, but not to the actual interesting money yet. Hero has 105K, 5th or so in the tournament, but several of the other largest stacks are at his table.

Don't have the actual hand history at hand, so this is from memory, but relevant stacks:

Hero (105K), 3 off the button, has JJ.
Villain (90K), in the CO.

Preflop, folded to hero, who raises to 15K, called only by villain.

Flop comes KT7, rainbow. I figure I shouldn't be looking to make this a big pot with an overcard on board and villain having a stack that can cripple me, but at this point any bet that's a noticable chunk of the pot is also a decent chunk of my stack. I bet 12K, figuring that should give me some idea where I stand. Villain just calls.

Turn was a blank, something like a 4 of the 4th suit. I check, figuring I'm behind villain's likely range at this point and planning to lay down to significant action. Villain surprises me and checks behind.

River is a jack, giving me a set. How do you play from here? About 61K in the pot, 78K left in my stack, 63K left in his, winning this pot will make me tournament chipleader at almost 200K and put me in decent position to make the final table.

Comments on both the river and earlier play welcome.

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.