How do _you_ decide when to bluffcatch and when not to? Toppair 3b pot OOP

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How do _you_ decide when to bluffcatch and when not to? Toppair 3b pot OOP

Blinds: $1.00/$2.00 (6 Players) BN: $836.10
SB: $313.27
BB: $590.88
UTG: $227.54
MP: $246.88
CO: $253.09 (Hero)
Preflop ($3.00) Hero is CO with Q K
2 folds, Hero raises to $5.00, BN raises to $15.36, 2 folds, Hero calls $10.36
Flop ($33.72) 6 J K
Hero checks, BN bets $10.89, Hero calls $10.89
Turn ($55.50) 6 J K 4
Hero checks, BN bets $41.87, Hero calls $41.87
River ($139.24) 6 J K 4 3
Hero checks, BN bets $767.98 and is all in, Hero
... has 184$ left

So Situation is as follows:
1,7k hands on villain - standardish regular with loose-agressive tendencies
3bets hero 21% on the BU so far (and 13% overall)
5.9 TOT 5b range

The high 3bet and high 5b% so far make me think that flatting pre here is best and folding I think is definitely too weak

Flop clear, even though there probably might be arguments for a checkraise given Equitydistribution and small cbet size

Turn easy!?

River meh and I am really unsure what data points I should use here to determine my call frequency / calling hands.

I probably never have AK here given his preflop tendencies... same goes for JJ, though for some reason I like flatting with JJ here a lot and I would certainly get to the river with it.
Then I have 66

Good thing is I unblock all FDs
Bad thing is 57 comes in

I need 36% equity:

and this is what I kind of could come up with...

Board: Kd6dJh4c3h
Equity Win Tie
CO 35.14% 35.14% 0.00% { KsQc }
BU 64.86% 64.86% 0.00% { KK+, JJ, KJs, 64s, AdQd, AdTd, QdTd, Td9d, Td8d, 9d8d, Ad7d, 8d7d, Ad5d, Ad4d, Ad3d, Ad2d, AKo, KJo, QdTs }

...which already seems to be kind of a stretch, doesn't it... needing him to shove almost every diamond combo every time....

In game I was kind of like "well with what better hand do I ever end up here?"...

But the analysis seems to indicate that especially against a loosish 3better with more 64, 57 going on that we probably have to wait for AK/KJ/JJ here to call!?

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