PS 16$ KK early, Check behind the Flop

[Seeeno]

First : Push PF ?
As played, what do you think about the Check behind at the Flop ? When I just push all-in, every better hand will call, all other hands will fold. I may induce a bluff or may give villain the 2. best hand.

PokerStars No-Limit Hold'em Tourney, Big Blind is t100 (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

UTG (t1590)
Hero (t1375)
CO (t2665)
Button (t2445)
SB (t4635)
BB (t790)

Preflop: Hero is MP with K[img]/images/graemlins/diamond.gif[/img], K[img]/images/graemlins/club.gif[/img].
<font color="#CC3333">UTG raises to t200</font>, <font color="#CC3333">Hero raises to t500</font>, <font color="#666666">2 folds</font>, SB calls t450, <font color="#666666">1 fold</font>, UTG folds.

Flop: (t1300) A[img]/images/graemlins/diamond.gif[/img], 3[img]/images/graemlins/spade.gif[/img], 9[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks, Hero checks.

Turn: (t1300) J[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">SB bets t600</font>, <font color="#CC3333">Hero raises to t875</font>, SB calls t275.

River: (t3050) 9[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>

Final Pot: t3050