How should I have played this hand?

[JoshNjuice]

I would appreciate some feedback on every street for this hand. What, if anything, should I have done differently?

This is the end of a 2-table $20+2 SNG on Stars.

Reads: Button is playing decent short-stack poker and has gotten lucky to double up a few times. He barely eeked into the money playing a little tighter than he should have. Since we made the money, he's been all-in maybe 3 times (it's been probably 12 hands), twice on the button (my BB); I've folded to his previous all-ins. SB has been pretty solid, but he has a little gamble in him. I usually have a good feel for the strength of his hand.

The stack sizes are important here. I have the button covered, but am covered by the SB. My goal is to win the SNG if possible.

Thanks in advance!

JoshNjuice

PokerStars No-Limit Hold'em Tourney, Big Blind is t200, ante is t25 (4 handed) converter

saw flop|<font color="#C00000">saw showdown</font>

<font color="#C00000">Hero (t4295)</font>
UTG (t14971)
<font color="#C00000">Button (t1869)</font>
<font color="#C00000">SB (t5865)</font>

Preflop: Hero is BB with A[img]/images/graemlins/spade.gif[/img], Q[img]/images/graemlins/heart.gif[/img].
<font color="#666666">1 fold</font>, <font color="#CC3333">Button raises to t1844</font>, SB calls t1744, Hero calls t1644.

Flop: (t5307) T[img]/images/graemlins/diamond.gif[/img], 7[img]/images/graemlins/heart.gif[/img], A[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">SB bets t600</font>, <font color="#CC3333">Hero raises to t2426</font>, SB calls t1826.

Turn: (t10159) K[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(3 players)</font>

River: (t10159) 6[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(3 players)</font>

Final Pot: t10159
<font color="#009B00">Main Pot: t5307, between Hero, Button and SB.
Side Pot: t4852, between Hero and SB</font>

[Blindcurve]

My first thought was you need to overpush and threaten the SB with a crippling.

The thing is, though, the SB's smooth call indicates either a lot of strength or a gamble. With your read, it would seem to indicate strength--his hand is big enough to allow you to come in. In his position, I'd only do this with AA, KK maybe QQ. The other thing is, if you miss the flop, are you folding and leaving yourself with 11-12 BB's? If you fold now, in the face of possible superstrength in the SB, you are still in a comfortable position to play against the other two stacks.

So, I think I'd fold and let them go at it. If I were going to play, I would reraise all in, on the off chance SB is gambling or can find a fold.

My caveat: This advice feels weak tight. 4-handed, AQ is a big hand.

-D.