4bet pot KK bad flop

You block AK and I don't see many weaker Ax flatting vs 4bet. Some AQs might be still there though. But so are JJ,TT.
He might be stabbing you because you check?
Check folding might be ok but what do you think about cbetting here?

Villain seems aggressive - his range is wider. I would cbet flop, then give up. But I think by checking OTF, we are getting into awkward spot. As played I call and again check OTT, if he bets again, fold, it´s A most of the time imo.

this is very annoying. i'm not sure why the Q is so bad though as it blocks some AQ combos which should be a decent part of a 3b/c range that value bets flop..
i feel like you can x/c once if you x/c down some Ax+ in this spot

If you do no want to commit, you can c-bet 1/3 pot here.

Cb 1/4 or x/f

5 / 8ths pot c-bet then cross yer fingers and close yer eyes

It is a 4bet pot, smartass.

For check-calling, how often does it go check-check turn, check-check river (or we hit)? Probably not often enough (which would be about 25% of the time). Blockers or not, he hit that flop.