1/2NL live - KK river play

[Will_Son]

1/2 NL live at a full table.

- I'm UTG+1 with $650.
- MP's play has been a strange mix of extremely tight and erratic. He'd muck for two orbits and then raise 72o in EP. Then he'd muck for three orbits and raise 83o. He has $600. Really quiet. Think he might be drunk.
- LP is a middle-aged asian dude. He just sat down a few hands ago and he has $300.

I raise KK to $12. MP pauses for a second or two and calls. LP calls relatively quickly.

Flop is 56Q rainbow. I bet $30, MP calls and LP calls.

Turn is a 3 of diamonds putting two diamonds on board. I check, MP instabets $50, LP pauses and calls, I call.

River is a 2 of diamonds. I check, MP bets $100, and LP snap-calls. My play?

Comments about other streets? I think I maybe should have check-raised the turn but we were deep and I thought I'd try to keep the pot small for the river.