5NL:KK vs set?

[Civi]

This is only the third hand the villain had played at my table. In the last few sessions I've had my raises called only to be find out the other player had a set etc.

Quite clearly I'm having problems spotting them as they come up. I've posted this hand to see what the players think about how I played this hand. And what they think the villain has.

Party Poker - No Limit Hold'em Cash Game - $0.02/$0.04 Blinds - 9 Players - (LegoPoker HH Converter)

SB: $6.28
BB: $2.00
UTG: $5.07
UTG+1: $5.23
MP1: $1.94
MP2: $5.95
MP3: $4.80
CO: $1.94
Hero (BTN): $4.94

Preflop: Hero is dealt K[img]/images/graemlins/diamond.gif[/img] K[img]/images/graemlins/club.gif[/img] (9 Players)
UTG calls $0.04, 2 folds, MP2 calls $0.04, MP3 calls $0.04, CO calls $0.04, <font color="red">Hero raises to $0.32</font>, 3 folds, MP2 calls $0.28, 2 folds

Flop: ($0.82) Q[img]/images/graemlins/heart.gif[/img] 3[img]/images/graemlins/spade.gif[/img] 9[img]/images/graemlins/heart.gif[/img] (2 Players)
MP2 checks, <font color="red">Hero bets $0.82</font>, MP2 calls $0.82

Turn: ($2.46) T[img]/images/graemlins/spade.gif[/img] (2 Players)
MP2 checks, <font color="red">Hero bets $2.34</font>, MP2 calls $2.34

River: ($7.14) T[img]/images/graemlins/club.gif[/img] (2 Players)
MP2 checks, Hero??