how could i have played AK better?

[Mariogs379]

PokerStars No-Limit Hold'em Tourney, Big Blind is t200 (6 handed) converter

BB (t640)
UTG (t1775)
Hero (t4085)
CO (t2630)
Button (t2100)
SB (t2270)

Preflop: Hero is MP with A[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/diamond.gif[/img].
<font color="#666666">1 fold</font>, Hero calls t200, <font color="#666666">2 folds</font>, <font color="#CC3333">SB raises to t400</font>, BB calls t200, <font color="#CC3333">Hero raises to t4085</font>, SB calls t1870 (All-In), BB calls t240 (All-In).

Flop: (t6995) 9[img]/images/graemlins/heart.gif[/img], 5[img]/images/graemlins/club.gif[/img], J[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(3 players, 2 all-in)</font>

Turn: (t6995) J[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(3 players, 2 all-in)</font>

River: (t6995) 4[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(3 players, 2 all-in)</font>

Final Pot: t6995

Results in white below: <font color="#FFFFFF">
BB has 4d Qh (two pair, jacks and fours).
Hero has Ah Kd (one pair, jacks).
SB has Td Tc (two pair, jacks and tens).
Outcome: SB wins t5180. Hero wins t1815. </font>

I believe i played this correctly because i would have had him dominated if he had any ace besides another AK and itd be about a coinflip if he had a pair. plus i read the middle player for weak given his limp and calling off for the rest of his chips...what do you all think?
how should i have played it?
-Mario