KK, should I have checked the flop?

You could stab and try to get him fold TT-QQ but the question is will he even fold them. This guy is an obvious fish (that 3bet size o.O) and you're inflating pot in which maniac could scare you off with some silly bluffs OTT/OTR.
I personaly like it as played - ace is highly probable in his range.
Good fold

I think checking the flop is ok. You don't have to cbet for value, because you may be behind, also you can't cbet as a bluff because you won't get better hands to fold.

You don't have to protect because if you're not behind, there's no high card that could come on the turn. Villain probably doesn't have a straight draw, and the board doesn't offer other draws yet.

About folding the turn, I don't know. Villain's 3-bet range from the small blind is not that narrow. A lot of people would bet on that board after the pre flop agressor checked. I think I would call.

We should cbet this flop. Dry flop with high card should be attacked.

You can cbet this flop. As played your fold is too tight.

We can def cbet here OTF. If called, we can evaluate turn easily as we have position. However, keep in mind that the calling range from SB is often strong.

Thanks for the replies everyone!

Qq

I don't mind checking back on this board with the intention of calling the turn. In this case he bets turn really big, so I guess folding is fine. I don't think we have to attack those flops with midle strenght hands every time. We can also check back some AX from time to time and bluffcatch on later streets.