Three-bet the turn with one pair?

[cartman]

Assume that villain is loose and aggressive. Not a maniac, but certainly capable of checkraising the turn with top or middle pair and also capable of checkraising with a draw, especially on a board he thinks I missed. I don't know what a turn cap or river 3-bet from him would mean. He will defend his BB with almost any two.

PREFLOP:
Hero open-raises in the CO with A[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/heart.gif[/img], only the BB calls.

FLOP: J[img]/images/graemlins/spade.gif[/img] 7[img]/images/graemlins/diamond.gif[/img] 4[img]/images/graemlins/club.gif[/img]
BB checks, Hero bets, BB calls.

TURN: Q[img]/images/graemlins/diamond.gif[/img]
BB checks, Hero bets, BB raises, Hero?


Here is my dilemma. I feel like I have the best hand often enough here that I need to put some more bets in at some point, either by 3-betting the turn or raising the river. The problem is that I also feel like it is borderline criminal to fold an overpair heads up unless the board is REALLY bad. But 3-betting the turn opens me up to a cap and raising the river opens me up to a 3-bet, both of which I feel obligated to call.

What do you guys think?

What would your line be if you had A[img]/images/graemlins/spade.gif[/img] Q[img]/images/graemlins/heart.gif[/img] instead?

Thanks,
Cartman