Overpair on paired board

[chucksim]

Here's a situation I've been having trouble with lately.

Party 1/2. Let's say you are in early position with Q[img]/images/graemlins/heart.gif[/img] Q[img]/images/graemlins/club.gif[/img]. You raise first in, button calls, and BB calls. Flop comes

J[img]/images/graemlins/diamond.gif[/img] 7[img]/images/graemlins/spade.gif[/img] 7[img]/images/graemlins/heart.gif[/img]

BB checks, I bet, Button folds, and BB check-raises.

Hero?????

What's your thinking here? In my mind, most likely, he's check-raising the J. If he weren't a blind, I'd be less inclined to believe he has a 7 and I'd three-bet. Assume he's a non-retarded, typical Party 1/2 player.

What's your line and, if you three-bet, what do you do if he caps?