Flopped the Nuts- Help Me Build a Pot

From today's $10 deep stacks tournament. It's the first time I've ever played this tourney, so while I have some cash game experience, I'm somewhat new to deep play. Here's the hand:

PokerStars No-Limit Hold'em Tourney, Big Blind is t800 (9 handed) converter

MP1 (t11280)
MP2 (t42686)
MP3 (t93000)
CO (t39900)
Button (t14721)
SB (t46875)
Hero (t65582)
UTG (t34068)
UTG+1 (t114933)

Preflop: Hero is BB with K[img]/images/graemlins/heart.gif[/img], A[img]/images/graemlins/club.gif[/img].
<font color="#666666">5 folds</font>, <font color="#CC3333">CO raises to t1600</font>, <font color="#666666">1 fold</font>, SB calls t1200, <font color="#CC3333">Hero raises to t5000</font>, CO calls t3400, SB folds.

Flop: (t11550) A[img]/images/graemlins/diamond.gif[/img], K[img]/images/graemlins/diamond.gif[/img], A[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets t3000</font>, CO calls t3000.

Turn: (t17550) 6[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">CO bets t6400</font>, <font color="#CC3333">Hero raises to t20000</font>, CO folds.

Final Pot: t43950

I felt like a pocket pair was his most likely holding, so I was trying to think about how to get the most out of that hand. I think if he's got KK the money probably goes all in no matter what. A good player could maybe get away from AQ, given the line I took here, but on the whole I felt like the weak lead and turn check would be the best way to get bleed a hand like TT.

All good? Is there a better way to build a pot here?