Turned 2 pair against BB

[speakinintongues]

$5+$0.50 single table
PokerStars No-Limit Hold'em Tourney, Big Blind is t200 (4 handed) converter

BB (t3937)
UTG (t925)
Button (t5240)
Hero (t3398)

Preflop: Hero is SB with K[img]/images/graemlins/heart.gif[/img], J[img]/images/graemlins/heart.gif[/img].
Button folds, <font color="#CC3333">Hero raises to t500</font>, BB calls t300.

Flop: (t1100) J[img]/images/graemlins/spade.gif[/img], A[img]/images/graemlins/diamond.gif[/img], 8[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">Hero bets t700</font>, BB calls t700.

Turn: (t2500) K[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(3 players)</font>
Hero checks, <font color="#CC3333">BB bets t2000</font>, Hero calls t1998 (All-In).

River: (t6498) 3[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players, 1 all-in)</font>

Final Pot: t6498

Just got into the money last hand. Please critique my play on this hand. I was fairly certain he'd put me all in on the turn but not sure if he'd call my all in. He overbet the pot twice against my preflop raise previously (about 8x overbet at 25/50) when I checked the turn or flop.