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I disagree about AT being likely. It would frankly shock me to see AT, given the read. If he's tight and passive, why's he going to cap out of position with a crappy hand? I would expect to see AA then QQ, both of which beat Hero by the river. I would probably just call the turn c/r, because when I see the preflop cap/flop call/turn check-raise, it's nearly always AA. I'd then probably call down on the river, because I'm nearly incapable of folding KK here.

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I think an overpair other than AA is likely in this hand and here's why:

1. Your opponent waited 'til the turn to raise you against a coordinated board with a FD, this is a common play used to protect overs when the pot is big.

2. He didnt checkraise you or bet out on the flop which he probably would do with a set when the pot is 3 handed or more.

I just can't see why he wouldnt show more agression on a flop that's coordinated with a strong hand like AA or a set.