I arrived late to the party, but


Why oh why would you check/call this flop? If you checked this flop, your only intention is to raise any bet/bet&shove turn.

If he has a set, so be it. But he could most likely have TT-QQ here, or a badly played AK.
KK usually doesn't flatcall pf. It takes a brave man to call a 8bb bet pf raise&reraise with 77 or 44.