$3.50 45-man KK UP vs shorter stack

I don't like betting that board. If we put him on something like 22+,A9s+,KQs,AJo+,KQo based on his raise/call preflop, then he still has 41% equity on this board. BUT he's not going to call or raise any of the hands that you have beat (sometimes a flush draw, but the chances of him having that are low). He will hopefully bluff hands that he doesn't want to let go off like some of his pocket pairs, and maybe much worse. So I just check/call flop and see what the turn brings. If you never give him credit for a bluff in this spot then you can even check/fold the flop

ugly on one hand you don't beat much -> 22+ is unlikely -> i would say after he calls the big 3bet he has more often 88-jj here than 22-77 -> if he is really that bad to call that wide you need to check/call imo!
if his not and and has more ax/qx combinations in his range than bet/fold small imo like 180!