At what point should I have dumped my Aces?

The pot just got too big so I felt I couldn't fold even though I knew I was probably beat

Villain was 69/21/1.6

Cryptologic 1.00/2.00 Hold'em <font color="#0000FF">(6 handed)</font> link

Preflop: Hero is CO with A[img]/images/graemlins/club.gif[/img], A[img]/images/graemlins/spade.gif[/img].
UTG calls, <font color="#CC3333">Hero raises</font>, <font color="#666666">1 folds</font>, SB calls, BB calls, UTG calls.

Flop: (8.00 SB) 6[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/heart.gif[/img], 6[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(4 players)</font>
<font color="#CC3333">SB bets</font>, <font color="#CC3333">BB raises</font>, UTG calls, Hero calls, <font color="#CC3333">SB 3-bets</font>, BB calls, <font color="#CC3333">UTG caps</font>, Hero calls, SB calls, BB calls.

Turn: (12.00 BB) 7[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(4 players)</font>
<font color="#CC3333">SB bets</font>, BB folds, <font color="#CC3333">UTG raises</font>, Hero calls, <font color="#CC3333">SB 3-bets</font>, <font color="#CC3333">UTG caps</font>, Hero calls, SB calls.

River: (24.00 BB) 5[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(3 players)</font>
SB checks, <font color="#CC3333">UTG bets</font>, Hero calls, SB calls.

Final Pot: 27.00 BB.
Results in white below:<font color="#FFFFFF">
UTG has 7s 6s (A Full House, Sixes full of Sevens)
UTG wins 25.75 BB.
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