Hello. Curious if I should be checking this flop. My bet/call vs a range of 8xxx is a -EV punt. Should I be preferring to XC this flop blocking the 2? Is my BC fine? Note CO is a passive rec and BTN is LAG reg.

Preflop went:

CO limp, BTN 3x, we 3b POT in BB, both call. Then we Bet-Call flop in a spot where I think I punted.

Blocking the 2 seems useful, but having NFD, what else is BTN jamming if not 8x (and sometimes they have quads)? Having to bet-fold makes me think that cbetting is an error.