SCOOP $215, flop continuing range vs Setherson2 check-raise

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SCOOP $215, flop continuing range vs Setherson2 check-raise

Blinds: t50/t100 (9 Players) SB: 4,030
BB: 4,952
UTG: 10,769
UTG+1: 4,585
MP: 4,752
MP+1: 9,827
MP+2: 3,483
CO: 4,970
BN: 7,494 (Hero)
BB here is RIO coach Setherson2, Seth Davies. Would be interesting to read his comments if he sees this hand. SB is also a pretty aggressive and good reg.
Preflop (150) Hero is BN with K T
6 folds, Hero raises to 253, SB folds, BB calls 153
I'm opening to ~2.5x here to make it harder for the blinds to realise equity since they're both good players. Range is probably a little tighter than usual, maybe in the 35% region. Setherson defends, which I expect him to do quite wide - his 3-betting range here I would think is quite polar, not sure exactly what he will expect of my response ranges so I don't know if he would be making any exploitative adjustments there.
Flop (664) 6 J J
BB checks, Hero bets 312, BB raises to 762, Hero folds
I think my c-bet sizing is fairly straightforward, I'm c-betting most of my range here but not all of it. Do you guys prefer reducing our sizing to allow ourselves to c-bet our entire range? I would be checking back a mixture of some A high hands, some air, and the occasional KK/AA/Jx+ type hand, although I'm aware that it's questionable as to whether I would actually be checking those back in-game even though I say I would be. It's one thing to say your flop checking range is protected and another thing to actually protect it.

When he check-raises, I'm curious about what you guys expect his range to be (or if he's able to provide input, what his range would actually be). I would tend not to have much of a check-raising range on a board like this so it's hard for me to interpret - I don't know whether he'd be more likely to check-raise a value-heavy range here because he expects me to never give him credit for Jx, or whether he's mostly check-raising a bluff-heavy range because he knows how much air I'm c-betting.

When it comes to building a continuing range, I assume all Jx and all 77+ are in there, so what would the next best hands be? I'm guessing stuff like KQs with a backdoor flush draw, maybe some other backdoor FDs that have live cards vs some of his bluffs...I sort of expect his bluffing hands to be overlapping a little bit with the weakest part of my continuing range, so perhaps there's an argument for folding more often since the times where I have the bottom of my continuing range (I thought about continuing with KTcc here) are perhaps going to be the times when he more often has value, but then I do block his KJ/JT here, so...I'm not sure.
Final Pot BB wins 1,288

Really curious for some input from you guys about what you would continue with here. I'm going to run it through a solver and see what it says.

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