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$100 6max, considering heroing river with K high in 3-bet pot

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$100 6max, considering heroing river with K high in 3-bet pot

Blinds: t80/t160 (6 Players) BN: 5,643
SB: 12,003 (Hero)
BB: 7,179
UTG: 5,829
MP: 9,717
CO: 5,020
Villain in this hand is a good reg with a long history of solid results, but he plays reasonably straightforwardly. It's likely he considers me to be a little tricky or station-y based on previous hands, but I could be wrong about that.
Preflop (240) Hero is SB with K Q
3 folds, BN raises to 320, Hero raises to 844, BB folds, BN calls 524
I think 3-betting here is reasonably standard. I would rather do that than flat-call OOP here. I imagine villain is calling the 3-bet quite wide - he has reason to think he'll be able to play well versus me postflop in this spot, and I've been active enough that he will assume my range to be wide here. Calling range of something like 44-88, A2s-A5s, ATo-AJo, KTs+, 76s+, 97s+, KJo-KQo, perhaps QJo. The weaker aces I'm a little unclear on, I don't have much history of playing big pots with the guy so I don't know much about what kind of hands I expect him to 4-bet/fold.
Flop (1,968) A 7 9
Hero bets 1,121, BN calls 1,121

Since I imagine villain is going to expect me to c-bet this flop very often and there are a reasonable number of bluffs in my range, I go fairly big, with a sizing that sets up a potential turn shove. Villain is likely calling with any Ax, any 7x or better, any gutshot, any spades, and probably floating sometimes with some one-spade broadway hands like KsQx/KsJx/QsJx or broadway hearts.
Turn (4,210) A 7 9 7
Hero checks, BN checks
With only one PSB behind, I think there's a chance villain could check back some reasonably strong hands here for the sake of waiting until the river to go for value. I also think he would be unlikely to simply expect me to c/f a hand like TT-KK here, so there's a couple of conflicting ideas in my head at this point. He might not bluff his floats right away if the latter is the case.
River (4,210) A 7 9 7 7
Hero checks, BN bets 3,658 and is all in, Hero folds
I was pretty much giving up when I checked, but when he tanked for a while before shoving, I thought twice about it. Theoretically K high isn't too much different from KK here since I'm pretty much bluffcatching - I guess the two main questions are the likelihood of him flatting certain Ax hands preflop which would shift his range towards value on the river, or the possibility of him valuebetting worse than Ax/7x on river, like valuebetting T9 or something, but I think that's less likely.
Final Pot BN wins 4,210
I ended up folding, but I did give some thought to calling it off here. I doubt I would have check-folded KK here, so perhaps I should have called K high? I'm really not sure.

Thanks guys, looking forward to input.

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