3 bet pot OOP in which I fold the overpair to a river jam on a nasty small card board

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3 bet pot OOP in which I fold the overpair to a river jam on a nasty small card board

Blinds: $0.25/$0.50 (6 Players) BB: $147.05
UTG: $61.96
MP: $78.10
CO: $50.98
BN: $52.00
SB: $96.00 (Hero)
Villain is 17/14; RFI is 20% from cutoff. Folds to 3b 50%.
I don't know what he calls three bets with but he will three bet mid connecting cards and low pocket pairs.
He- and I say he because his icon is the cop from Die Hard - is capable of bluffing the river and I have seen him reraise and fold preflop as well, so his ranges are tight but have some balance to them.
Preflop ($0.75) Hero is SB with K K
UTG folds, MP raises to $1.25, 2 folds, Hero raises to $5.25, BB folds, MP calls $4.00
Flop ($11.00) 6 5 3
Hero bets $3.75, MP calls $3.75
Turn ($18.50) 6 5 3 T
Hero checks, MP bets $14.06, Hero calls $14.06
River ($46.62) 6 5 3 T 4
Hero checks, MP bets $55.04 and is all in, Hero folds

Solver said bet what I bet in my range bigger on flop - I guess I see why against villain's range; mix bets and checks on turn; river jam is straights and air to which KK folds mostly. Interestingly, KK check raises on the turn if the bigger bet is used on the flop.

I think my decision comes down to "what will the villain bet?" My hand, unfortunately, is kind of the top of my "abc" range besides pocket 77 and the rare 78s and everything less than those is vulnerable to bluffs. BUT my opponent could also be value betting QQ!

If it weren't for the huge size I feel like this is an easy call but this villain knows enough to jam with bluffs.

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