I'd bet the river and pray he wasn't sandbagging and then raises you. He may have been chasing overcards and you hope he'd fold to the river bet.

If he is that tight though I wouldn't be surprised if he showed you a pocket pair 10 or higher. (EDIT: 10's or JJ since he didn't cap pf.)

I'd be weary of 3-betting pf in the BB because you're first to act on the rest of the betting rounds. But since you did I'd bet to the river.