three way final hand

PokerStars No-Limit Hold'em Tourney, Big Blind is t200 (3 handed) converter

Hero (t9772)
BB (t4895)
Button (t3333)

Preflop: Hero is SB with 6[img]/images/graemlins/spade.gif[/img], T[img]/images/graemlins/spade.gif[/img].
Button calls t200, Hero completes, BB checks.

Flop: (t600) 6[img]/images/graemlins/club.gif[/img], 3[img]/images/graemlins/spade.gif[/img], 4[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">Hero bets t600</font>, <font color="#CC3333">BB raises to t2000</font>, <font color="#CC3333">Button raises to t3133</font>, <font color="#CC3333">Hero raises to t9572</font>, BB calls t2695 (All-In).

i'll be honest and say i didn't completely think it through after the button went all in. he'd been pushing alot of hands that didn't get shown down, so i figured he might be on a flush draw.

the bb is the one i gave little thought to. he'd been very tight the entire final table. and i should have read his reraise as legitimate strength.

what little thought i did put into it was that bb had a better 6 and the button had a flush draw. if this is indeed my read, is a fold warranted here? i figured i was ahead of one and had outs to draw out on the other, but my flush outs might possibly be no good.