Definitely not spew imo. Folding here would require a very strong read on villain, which you don't have. I like your range, although I don't think KK would have 3-b the flop. Villain could also have something like AsQs, AsTs depends how he plays with combo draws.
I also like your raise on the flop. I would have 4-bet all-in though, because a flush/straight card could kill your action on the turn/make you hate life.
I don't think you can worry about set over set unless you're even deeper than this, though someone else might disagree. I felt this every time.