AK makes TPTK: Drawing Virtually Dead?

[BoxTree]

Commerce 20/40, 9-handed

Hero is UTG with A[img]/images/graemlins/club.gif[/img]K[img]/images/graemlins/heart.gif[/img].

Hero raises, Fold, Fold, MP2 cold-calls, Fold, Fold, Button cold-calls, SB folds, BB calls.

Flop (4 players, 8 sb): A[img]/images/graemlins/spade.gif[/img]7[img]/images/graemlins/spade.gif[/img]4[img]/images/graemlins/heart.gif[/img]

BB bets, Hero raises, MP2 3-bets, Button folds, BB folds, Hero...?

Notes on MP2: She's a highly predictable, very tight player (but cold-calls too much) who is very rarely over-aggressive. I'd say there's just shy of a 100% chance that she has A7s, A4s, 77, 44, or AK. She wouldn't 3-bet the flop with any other holding.

Given that there are six ways for her to have a set and three ways for her to have two-pair (Ad7d, Ad4d, Ah7h), should I see the turn getting 14:1? If I catch an 8-Q on the turn, should I see the river getting 8.5:1 to improve to a better two-pair?

I feel like I should be folding this flop. Too weak?

Against a tougher opponent who knows that I'm likely raising the flop with AK-AJ and possibly raising with TT-KK, I'm sticking with this hand and may get fancy later on. A tougher player could 3-bet me with TT/JJ, AQs/AJs, or perhaps a straight or flush draw. But MP2 would do no such thing. Her 3-bet says, "I can beat everything but AA."