Pocket Kings and no clue at all

I seriously had no idea at all of how to play this, but I'm pretty sure what I did was pretty bad. Any ideas for next time?

The CO was 39/23/3.27 over 75 hands, and the button was 31/16/1.43 over 30 hands.

PokerStars 2/4 Hold'em (6 handed) FTR converter on zerodivide.cx

Preflop: Hero is SB with K[img]/images/graemlins/diamond.gif[/img], K[img]/images/graemlins/heart.gif[/img].
<font color="#CC3333">UTG raises</font>, <font color="#666666">1 fold</font>, <font color="#CC3333">CO 3-bets</font>, <font color="#CC3333">Button caps</font>, Hero calls, <font color="#666666">1 fold</font>, UTG calls, CO calls.

Flop: (17 SB) 6[img]/images/graemlins/spade.gif[/img], 3[img]/images/graemlins/diamond.gif[/img], A[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(4 players)</font>
Hero checks, UTG checks, CO checks, <font color="#CC3333">Button bets</font>, <font color="#CC3333">Hero raises</font>, UTG folds, CO calls, Button calls.

My thoughts on the flop checkraise were that the pot is really big, it was checked through to the button, and maybe there's a tiny chance I can get a weak ace to fold here. In retrospect, though, this seems like a stretch.

Turn: (11.50 BB) 9[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(3 players)</font>
Hero checks, <font color="#CC3333">CO bets</font>, Button folds, Hero folds.

On the turn, my thoughts were, screw it, I'm beaten.

Final Pot: 12.50 BB