KK on a AJ6 flop against a big stack

[FishInAPhoneBooth]

Party Poker No-Limit Hold'em Tourney, Big Blind is t200 (10 handed) converter

SB (t17697)
BB (t2108)
<>< (t4416)
UTG+1 (t11434)
UTG+2 (t6409)
MP1 (t7762)
MP2 (t3487)
MP3 (t9265)
CO (t16023)
Button (t7796)

Preflop: <>< is UTG with K[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/club.gif[/img].
<font color="#CC3333">&lt;&gt;&lt; raises to t500</font>, <font color="#666666">5 folds</font>, CO calls t500, <font color="#666666">2 folds</font>, BB calls t300.

Flop: (t1600) A[img]/images/graemlins/heart.gif[/img], J[img]/images/graemlins/heart.gif[/img], 6[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(3 players)</font>
BB checks, <font color="#CC3333">&lt;&gt;&lt; bets t425</font>

I feel like I cost myself 400 extra chips with 0% chance of winning the pot. Is the best way to handle this situation? Is a simple check followed by a fold optimal? I really had no relevant reads.