AQ in 4bet pot on a K high flop. Bet or check?

[Chaser8]

The villain, which we will call "JerkOff", and I played this hand:

Full Tilt Poker, $2/$4 NL Hold'em Cash Game, 6 Players
LeggoPoker.com - Hand History Converter

MP: $793.70
Hero (CO): $394
BTN: $514.30
JerkOff: $425.50
BB: $406
UTG: $480.07

Pre-Flop: J[img]/images/graemlins/club.gif[/img] T[img]/images/graemlins/diamond.gif[/img] dealt to Hero (CO)
2 folds, <font color="red">Hero raises to $14</font>, BTN folds, <font color="red">JerkOff raises to $50</font>, BB folds, <font color="red">Hero raises to $132</font>, JerkOff calls $82

Flop: ($268) 6[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/heart.gif[/img] J[img]/images/graemlins/diamond.gif[/img] (2 Players)
JerkOff checks, Hero checks

Turn: ($268) 8[img]/images/graemlins/diamond.gif[/img] (2 Players)
JerkOff checks, Hero checks

River: ($268) 9[img]/images/graemlins/club.gif[/img] (2 Players)
JerkOff checks, <font color="red">Hero bets $262 and is All-In</font>, JerkOff folds

I shoved the river for a psb to get value from a 9 or maybe even A high. I don't think he checks flop turn and river with anything that beats my J. Shortly after, this hand happened:

Full Tilt Poker, $2/$4 NL Hold'em Cash Game, 6 Players
LeggoPoker.com - Hand History Converter

UTG: $572.35
MP: $400
Hero (CO): $631.60
BTN: $389
SB: $424.60
JerkOff: $406

Pre-Flop: Q[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/club.gif[/img] dealt to Hero (CO)
2 folds, <font color="red">Hero raises to $14</font>, 2 folds, <font color="red">JerkOff raises to $52</font>, <font color="red">Hero raises to $136</font>, JerkOff calls $84

Flop: ($274) 9[img]/images/graemlins/diamond.gif[/img] 4[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/diamond.gif[/img] (2 Players)
JerkOff checks, Hero?

The villain's stats are 20/16/3. He has already 3bet me several times before these two hands took place. I have been folding to his 3bets up until when I 4bet with JT. He called both my 4bets fairly quick, which means he does not like to fold whatever he 3bets with.

Given our history, how do we play the rest of hand 2? I feel like checking and re-evaluating turn, but that might be too weak. Do we have enough fold equity to fold out QQ JJ TT here?