i think imo it could be a bad bluff attempt on his part. like u said when you x/c each st it looks like what you have a lot. so maybe even tho he didn't fire turn he thinks he can get u to fold none k hands river. otherwise he's going for value with a weak king. I think spots like this only you will no what is "right" like what u were feeling or saw etc is gonna make a lot of the decision. I think mathematically you can call all day esp with how weak are hand looks on the river. with all his bluffs or 99 tt a9thruaq and all wired hands trying to steal pre then cbet steal flop kinda give up on turn then try again on river lol. your winning with a call here more than 33% of the time so call is fine but wouldn't think it was bad if ya folded

hmmm...wanted to calculate a MDF for this spot. But while constructing a decent range for OP i realised that there is only about 8-12 Kx combos that hero should have in his range here (KTs+ or KJs+), while still having abut 78 combos in an average flatting range here: JJ-77, AQs-ATs, KTs+, QTs+, JTs, T9s, 98s, 87s (maybe a little wide for beeing OOP and no strong flats like AA/KK)

That said i guess we have to defend a lot of stuff in this range vs his riverbet for not beeing heavily exploitable!!!

We need to call about 29,6% to BE

That would be 24 combos: So any Kx (12), 99 (1), JJ (6), TT (6) would be 25 combos

But as said, if Villain is realising how unlikely it should be for us to have a K here i guess 25 Combos, maybe even including T9s (4) for defending 33% would be decent from a GTO perspective

But GTO on the side, i rarely see ppl playing these Bet/check/Bet lines IP as a bluff and OP´s line screams SDV and there was no FD OTF. I would even Ax expect to check back with SDV himself mostly here...Not sure if an "heavily exploitable" fold still would be the better play

I dont see why hed pot control AK/KQ, you block KJ, so which is more likely hes 3 betting KT- or bet/check/bet as a bluff. Both arent that likely imo given no reads (he could also just be slowplaying KK/99). Altho we need one to be less likely more than twice as often to call, which I dunno if its the case. Prolly really doesnt matter all that much what you do honestly. So id call for the read

Its likely not going to be a big mistake what you do here readless, I'd call just because he can have a lot of random stuff Btn vs co that took a free card on that turn but feels it should still bluff now like 78/89/QT hands