How would you play this hand?

[krazyace5]

Party Poker No-Limit Hold'em, $0.5 BB (6 max, 4 handed) converter (http://www.selachian.com/tools/bisonconverter/hhconverter.cgi)

SB ($76.04)
BB ($70.75)
Hero ($80.09)
Button ($112.08)

Preflop: Hero is UTG with K/images/graemlins/diamond.gif, K/images/graemlins/spade.gif.
<font color="#CC3333">Hero raises to $3</font>, <font color="#666666">2 folds</font>, BB calls $2.50.

Flop: ($6.25) 6/images/graemlins/diamond.gif, 8/images/graemlins/club.gif, J/images/graemlins/club.gif <font color="#0000FF">(2 players)</font>
BB checks, <font color="#CC3333">Hero bets $4</font>, <font color="#CC3333">BB raises to $8</font>, <font color="#CC3333">Hero raises to $15</font>, BB calls $7.

Turn: ($36.25) T/images/graemlins/club.gif <font color="#0000FF">(2 players)</font>
BB checks, <font color="#CC3333">Hero bets $13</font>, BB calls $13.

River: ($62.25) A/images/graemlins/spade.gif <font color="#0000FF">(2 players)</font>
BB checks, Hero checks.

Final Pot: $62.25

Results in white below: <font color="#FFFFFF">
BB has 9h Jh (one pair, jacks).
Hero has Kd Ks (one pair, kings).
Outcome: Hero wins $62.25. </font>

[Allinlife]

if you want to 3bet the flop, you need to raise to 30$ at least.

On turn, I would probably check behind.

I'd check behind that A too but if he checks to you on a blank, you can probably valuebet 1/2 pot bet vs KJ/QJ/AJ and fold to a check-raise.

[nietzreznor]

I agree, I think if you are gonna 3bet the flop you need to make it much more than $15 (which is basically a minraise).
As for the turn: do you have any reads? With 3 clubs out, and you not having K /images/graemlins/club.gif, I would want to bet here (like a bigger bet than you threw out there, 1/3 seems way too small. Either check or put a real bet out). It seems unlikely to me that villain made a flush (why min-checkraise flop on flush draw?), but I don't think you want to give a free card to a lone /images/graemlins/club.gif. of course, this is assuming you are ahead right now, which I think you *probably* are. But I guess this comes down to reads as well, there are plenty of people at these stakes who min-checkraise with junk, and plenty that need at least two pair.
I probably check behind river as well, not sure if you will get another call from anything you beat...