Double Suited Kings in 3b pot vs. Aces heavy range

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Double Suited Kings in 3b pot vs. Aces heavy range

BN: $100
SB: $118.96
BB: $156.36
UTG: $124.52
HJ: $190.18
CO: $134.96
Preflop ($1.50) (6 Players)
Hero was dealt 4 K K 6
UTG folds, HJ calls $1.00, Hero raises to $4.50, BN raises to $16.00, SB folds, BB folds, HJ folds, Hero calls $11.50
Flop ($34.50) 5 9 8 (2 Players)
Hero checks, BN checks
Turn ($34.50) 5 9 8 9 (2 Players)
Again I don't have many hands on the villain, so there is a chance my reads are way off, but at the time villain had pretty snug stats and I assumed that even if he was a generally more aggro player he'd be less inclined to three bet to try and keep the limped in the pot.

His flop check makes me think AA with nuts clubs or AA with a 9 unlikely and only have 32.5% equity vs. the nut worst aces. I have a lot of equity here, but I am not sure if I can proceed vs. a raise, especially if I bet on the smaller side. Pot calling seems like the simplest play, but I have no idea if it's the best play, it seems better than betting small and folding ot a shove and idk where check calling fits on this spectrum.

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