Villain just sit at the table. how do we play?

PokerStars No-Limit Hold'em, $0.50 BB (8 handed) Poker-Stars Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

UTG ($61.95)
UTG+1 ($49.75)
MP1 ($39.80)
MP2 ($50)
CO ($18)
Button ($72.35)
Hero ($36.95)
BB ($57.80)

Preflop: Hero is SB with K, A.
2 folds, MP1 calls $0.50, 2 folds, Button raises to $2.5, Hero calls $2.25, 1 fold, MP1 calls $2.

Flop: ($8) 9, 7, K (3 players)
Hero bets $5.5, MP1 calls $5.50, Button folds.

Turn: ($19) Q (2 players)
Hero checks, MP1 bets $10, Hero calls $10.

River: ($39) Q (2 players)
Hero checks, MP1 bets $15, Hero folds.

Final Pot: $39

I like a 3bet preflop. If you just call, you give great odds for MP1 to come along with whatever he's limping. A 3bet may just take it down there, which is fine. If button calls, you're still seeing a flop out of position, but odds are it'll be heads up and you'll take it down a lot of the time with a cbet whether you hit or not. The way you played it, if you miss you're pretty much check/folding.

But you hit, so that's good. I don't like the flop donk, especially into two people. You fold out the hands you beat, and make it pretty clear what you have. You wouldn't play a set or a draw like this, would you? Check to him, and see what he does.

Any reads on MP1? I probably bet the turn after leading the flop. You don't really want to let villain check behind if he's on a draw. If he's got a monster, he'll probably let you know by raising you. Donking the flop and checking the turn makes it harder to tell what any turn bet from him means.

As played I'd call the turn and fold the river, just like you did. That river card is pretty bad for you, and you've played your hand in a way that makes it seem unlikely you'll be ahead.

3bet preflop every time. Postflop is fine.

Just trying to put the villain on a range here: Limpcalls PF, so I put him on any PP or JT+ QT+ KT+ AT+ (yes, if he limcpalls in MP1 I will think he's a station until he proves otherwise.) What calls on the flop? Any set, any king, any straight draw and any flush draw.

Set has you beat.
King could have you beat (with KQ only)
The TJ straight draw got there with the straight. The QJ and QT draws got there with trips.
The flush also got there.

I probably take a b/f line on the turn and be a weak nit on the river and c/f