KQ pair of Kings Vs 2 pair

PokerStars No-Limit Hold'em, $0.02 BB (8 handed) FTR converter on zerodivide.cx

UTG ($1.01)
UTG+1 ($2.46)
MP1 ($2.04)
MP2 ($2.23)
CO ($4.91)
Button ($6.10)
Hero ($5)
BB ($2.89)

Preflop: Hero is SB with Q:heart:, K:heart:. MP1 posts a blind of $0.03.
2 folds, MP1 (poster) checks, MP2 calls $0.02, 1 fold, Button calls $0.02, Hero raises to $0.10, 1 fold, MP1 folds, MP2 calls $0.08, Button calls $0.08.

Flop: ($0.35) K:diamond:, 8:diamond:, 9:club: (3 players)
Hero bets $0.40, MP2 calls $0.40, Button folds.

Turn: ($1.15) A:spade: (2 players)
Hero bets $0.40, MP2 calls $0.40.

River: ($1.95) A:heart: (2 players)
Hero bets $0.40, MP2 calls $0.40.

Final Pot: $2.75

Clearly i got lucky here. I realised i was probably behind after he called the turn and my plan was to check-call a small bet on the river. When the next ace came it ment i was only behind to a set (still not too unlikely) so i made a small value bet which would be called by any 2pair or weaker K that had been calling me so far and would stop him trying to bluff me out with a missed flush draw.

Villain had well over 50% VPIP and hardly ever raised. The reason i made the river bet (and the others) is because he seemed very fishy and hardly ever raised so i believed he would call with very weak hands. Against most opponents i would have check-called a small bet on the river or check-folded his all-in

What would you do?

You over bet the flop with only TPGK against bad/fishy opponents who have position on you. What is your intention with this flop bet?

Any good player is going to slam in a big raise on the river after you've shown such weakness on the turn and river. That being said, you have a read which says this opponent is not good...and because of that, I think your river bet is a good one because it serves to block if your opponent does hold an A since you said he was so passive.

My line would be: Bet the pot on the flop, check/call the turn, check/call the river.