Daily 50 Grand, KK in LP, ugly board

[mlagoo]

PokerStars No-Limit Hold'em Tourney, Big Blind is t20 (9 handed) internettexasholdem.com

Button (t3500)
SB (t3130)
BB (t2990)
UTG (t2970)
UTG+1 (t2970)
MP1 (t2970)
MP2 (t3000)
MP3 (t2970)
Hero (t3060)

Preflop: Hero is CO with K[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/diamond.gif[/img].
<font color="#666666">5 folds</font>, <font color="#CC3333">Hero raises to t80</font>, Button calls t80, <font color="#666666">2 folds</font>.

Flop: (t190) 5[img]/images/graemlins/spade.gif[/img], 6[img]/images/graemlins/diamond.gif[/img], 4[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets t140</font>, <font color="#CC3333">Button raises to t300</font>, Hero calls t160.

Turn: (t790) J[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">Button bets t320</font>, Hero calls t320.

River: (t1430) 3[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">Button bets t440</font>, Hero folds.

Final Pot: t1870

Thoughts? This was super early in the tourney so no real reads. The river seems obvious (he almost never has a bluff here given previous streets, and he's not VBing a worse hand), but do you give more action on the flop or turn?