6/12 Borg - KK question

[anisotropy]

I was down on 12/26 playing 6/12 at the Borg when this hand occurred. I had been at the table a while, as had everyone else except the new guy I was up against. He had been there maybe a half hour and I hadn't seen him play too much except a few monsters. He rarely limped in, though.

I am in the SB with KK. MP1 limps, villain (button) raises and I 3-bet it. Everyone drops except BB and MP1 and villain.

Flop: 7 [img]/images/graemlins/spade.gif[/img] 8 [img]/images/graemlins/diamond.gif[/img] 3 [img]/images/graemlins/club.gif[/img]

Action is bet, fold, call, call. So now we're heads up.

Turn: 6 [img]/images/graemlins/heart.gif[/img]

Rainbow is complete. Action is bet, fold, raise by button (?) and I'm really confused. I think for a second about 3 betting, but instead just call. Is this bad? I don't think I should consider folding but I'll listen to arguments for that as well.

River: T [img]/images/graemlins/diamond.gif[/img]

I really don't like the 4 straight out there and check. He checks behind and <font color="white">shows AJd and MHIG.</font>

So questions are: should I fold/3-bet the turn? Should I bet the river? How badly did I misplay this?