One too many raises, or WAY too many raises?

[TightWad]

The point of this post is NOT to bitch about being 2-outered. I'm on like a 10-day streak of that, so I'm used to it, and plus anyone who hits as many backdoor draws as I do has NO right to complain. My question is how much did I overplay this hand? I don't think capping the turn was catastrophic, but after that should I have check-called the river, or bet and called a raise? I really can't help but feel that by the river, KK is just looking like way too much of a possibility to cap it, and yet I stubbornly did anyway. Another important point is that when I 3-bet his river raise, he'll almost certainly just call with a hand I have beaten (i.e. a rather overplayed AK or AA), and is unlikely to raise with anything I'm ahead of.

I don't know, I'm thinking the best line would be bet the river and call a raise, but maybe even that is going too far? Just check-call? What say ye?

Party Poker 3/6 Hold'em (10 handed)

Preflop: TW is BB with , .
4 folds, MP2 raises, 1 fold, CO calls, 2 folds, TW calls.

Flop: (6.33 SB) , , (3 players)
TW bets, MP2 calls, CO folds.

Turn: (4.16 BB) (2 players)
TW bets, MP2 raises, TW 3-bets, MP2 caps, TW calls.

River: (12.16 BB) (2 players)
TW bets, MP2 raises, TW 3-bets, MP2 caps, TW calls.

Final Pot: 20.16 BB

Results in white below:
TW has 2h 2c (three of a kind, twos).
MP2 has Ks Kh (three of a kind, kings).
Outcome: MP2 wins 20.16 BB.

-TW

[EscapePlan9]

I'd say bet-call the river. He could be overplaying AK. Whenever you have a set, you're usually the only person with one.

[Xaston]

It would have been a mistake for him to fold the flop, DID YOU SEE HIS IMPLIED ODDS!?

[TightWad]

TW in a hand = MASSIVE implied odds for everyone else