You have a good hand to Cbet and fire a 2rd barrel and a bad one for a 3st...
The sizings seem suboptimal pre and ott...I like ~4-4.5x pre with 70bbs and def bigger ~65-70% ott. When u 2barrel, your saying that you have a range adv/that the K helps you > btn, so it makes no sense not to bet big. You also have the Qc which makes it a little less likely that btn can continue.
Otr the Qc then becomes a bad blocker and you're too high in your range to bruff. You will have 87ss; 87dd; 87hh and ATs combos to use as bluffs, so I like b/b/checkfold.
Imo, dont worry about what villain will call with or fold. We only have a limited time to consider variables, so it's important to prioritize them. If you're playing perfectly then you'll make him indifferent (to call/fold), so who cares?