NL Cash Raised Pot TP 2nd Kick

[Megenoita]

Okay, I was playing a decent tag 1/2 NL HU FTP. About 10 minutes into the match, he started to 3-bet light--A5s, QJs that I saw. Now, I had folded up until this point, and I raised on the BTN, he 3-bet, I called with KQo. The flop came K x x with 2 clubs. He c'bet, and I called. On the turn, he thought (non-club x turn) and bet again, and I just put the rest in there (not much more).

Is this a spot where I should be able to fold? Is it standard to go broke here? Should I have not called pf? If not, how do I combat his light 3-betting?

Thanks,
M