Value bet KK on river in bloated pot?

[CobraGoat]

at work no HH.

FT, 6max 50NL.

Hero: $140
Villain: $110

Villain is complete calling station, worse than ive maybe ever seen, super loose passive, never raising, calling repeat huge bets with 2nd or 3rd pair etc. As an aside it seems like there are a lot more horrific players at 50NL than 25NL. Against most players I would probably not have built such a big pot on all streeets but this guy was amazingly bad (he only had a stack from ridiculous beats, his stack was yoyoing).

Hero in BB dealt KK.
Villain UTG limps, MP limps, Button limps and SB completes, i raise to $3.5. Villain calls and then MP shoves in for $10. Button and SB fold and I just call because I want to play a big pot with villain. Obviously villain calls. Pot is like $32.

Flop: Q[img]/images/graemlins/diamond.gif[/img]2 [img]/images/graemlins/diamond.gif[/img]2 [img]/images/graemlins/club.gif[/img]

I bet $27, villain calls.

Turn: 5 [img]/images/graemlins/club.gif[/img]

I bet $52, villain calls. At this point I am putting him on a Q or a PP below, maybe a FD.

River: 9 [img]/images/graemlins/heart.gif[/img]

What is my action here OOP? Shove? c/c? given the size of the pot and villains likely holdings i think i have to shove to maximize the value of my hand v. his range or should i be thinking to check down given that villain, despite being a station, has called two massive bets so far? I dont think there is any value in trying to induce a bluff, this villain seems much more likely to check behind with all worse hands.

THought on my flat call pre? Thoughts on my bet sizing on flop and turn?