why u check on flop？

Flopcheck looks fine to me as this board is highly preferable for Villains range.
But i guess i would still lean towards XR here even though Villains sizing sucks (as it looks kind of polarizing). I would prefer to go into XC-mode with strong NFD hands as they have much more SDV.
As we see its kind of annoying to loose to A-high OTR :/

I prefer cbetting flop and turn.
KhJh is a good hand to put in your double barrel bluff range to balance the times you have overpair or better.

I think the check on flop is solid and given villains bet size, I prefer calling over raising here. On the turn, I think we do have a nice spot to check-shove after the weird, mergy sizing (maybe I just dont understand the approach, but why would you polarize on flop and then merge on turn?).

I would consider going bigger preflop. Vs the 2bb open I would do 9bb and probably add 0,5bb for the slightly bigger than usual effective stacks.