AA ~250BB deep against aggression (I suck at poker)

[Vince.]

Villain is the reason I'm at the table, he is 43/17/3. Pretty loose preflop but haven't seen him get too out of line post flop. He's only CR'd the flop 2 times in his last 92 chances. I have no idea what to do here I am totally lost. I feel like if I push he is snap calling with a set. I'm not used to playing this deep.

Full Tilt Poker, $0.50/$1 NL Hold'em Cash Game, 4 Players
LeggoPoker.com - Hand History Converter

SB: $64.50
BB: $235.60
Hero (UTG): $324
BTN: $243.65

Hero posts $0.50
Pre-Flop: A[img]/images/graemlins/diamond.gif[/img] A[img]/images/graemlins/heart.gif[/img] dealt to Hero (UTG)
<font color="red">Hero raises to $4</font>, 2 folds, BB calls $3

Flop: ($8.50) 6[img]/images/graemlins/spade.gif[/img] 3[img]/images/graemlins/club.gif[/img] 4[img]/images/graemlins/club.gif[/img] (2 Players)
BB checks, <font color="red">Hero bets $6</font>, <font color="red">BB raises to $20</font>, Hero calls $14

Turn: ($48.50) 8[img]/images/graemlins/diamond.gif[/img] (2 Players)
<font color="red">BB bets $49</font>, Hero...