Overplayed AA or just lucky opponent draw?

[suckbot]

This isn't intended as a bad beat post, because I'd like to know whether I played this wrong.
Compliments of PokerGeek
PokerStars NL Hold'em Tournament - 100/200 Blinds (7 handed)

Starting Stacks
Seat 2: MP (Hero) (T6984)
Seat 3: LP (T3062)
Seat 4: CO (T4634)
Seat 5: Button (T6560)
Seat 7: Small blind (T5653)
Seat 8: Big blind (T7650)
Seat 9: UTG (T10969)

Preflop: Hero is MP with A[img]/images/graemlins/club.gif[/img], A[img]/images/graemlins/heart.gif[/img].
<font color="#666666">2 folds</font>, Hero raises (1000), LP folds, CO folds, Button folds, Small blind folds, Big blind calls (800)

Flop: (T2100) 5[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/heart.gif[/img], 9[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
Big blind checks, Hero bets (1600), Big blind raises (3600), Hero all-in (5959), Big blind calls (2359)

Turn: (T9659) J[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(0 players)</font>


River: (T9659) 8[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(0 players)</font>


Final Pot: T14218

Results in white below:
<font color="#FFFFFF">Big blind has 9d 9h (three of a kind, Nines)
MP has Ac Ah (a pair of Aces)
Outcome: Villian wins T14218
</font>
When I re-raised him on the flop, I'd hoped he was on a strong K or flush draw. I figured he wouldn't have called $800 with something as weak as K-9. But should I have been more cautious at this point? At that point, I didn't think a call was right. it was either push or fold. I'd love your thoughts.