KK against aggression

[Cheshire]

I am new to 1/2 and so far a marginal winner or loser. I have not played enough to really know yet.

Party Poker 1/2 Hold'em (9 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

Preflop: Hero is MP2 with K[img]/images/graemlins/diamond.gif[/img], K[img]/images/graemlins/club.gif[/img]. MP1 posts a blind of $1.
<font color="#666666">2 folds</font>, MP1 (poster) checks, <font color="#CC3333">Hero raises</font>, <font color="#666666">5 folds</font>, MP1 calls.

Flop: (5.50 SB) Q[img]/images/graemlins/spade.gif[/img], 9[img]/images/graemlins/spade.gif[/img], 2[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">MP1 bets</font>, <font color="#CC3333">Hero raises</font>, <font color="#CC3333">MP1 3-bets</font>, Hero calls.

Turn: (5.75 BB) A[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
MP1 checks, Hero checks.

River: (5.75 BB) A[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">MP1 bets</font>, Hero calls.

Final Pot: 7.75 BB

I think preflop and flop are pretty standard. Is this a clear check behind on the turn or is a free card too dangerous even though I might be behind? During the hand I really thought about raising the river for value but I just could not do it. Generally what is the villians range here and can I raise for value?

I am heading to sleep now, I will check in during the morning and see if anyone cares. If someone does then I will respond.