Call, either lead or raise (probably shoving depending a bit on villain's bet sizing) on the turn depending on what he does.
This is a pretty simple situation, from villain's perspective we've raised from late position when folded to, therefore he will assume there's a high chance we're stealing and although KQ isn't a huge hand he may not suspect we have as strong a hand as we do, and KQ would be at the higher end of the range he will be assigning us.
The flop is a good flop for a continuation bet, and as villain is a solid player he will know this, and more importantly he will know that we know this. Therefore what does our flop bet mean to him? Not a lot - it's entirely possible villain sees that we see it's a good flop for a c-bet and although we've missed the flop we're going to bet at it. Yes, we might have the K, but by checkraising (a) he is going to get us to fold if we don't have anything, and (b) a checkraise is such a show of strength we might fold a very weak K (although I'm not sure if villain would expect us to raise even when folded to in LP with potentially big trouble
hands like ~K5).
If villain actually had a huge hand here, he would be best served by leading, which on this sort of board would most likely be perceived by us exactly as villain perceives our lead - that is as a bet which is hoping to just take the pot down on a flop which is unlikely to have hit his hand. Alternatively, he could check-call, but check-calling on an unco-ordinated board like this is, to a thinking player who knows he's playing a thinking player, just as scary if not more so than a check-raise. Good players know the value of disguising their hand. Villain is representing huge strength here by checkraising - would he want to represent huge strength on an unco-ordinated board like this one if he actually was very strong? I dunno, I guess it depends on how many levels we're operating on, but the answer is 'probably not'.
Also, obviously there aren't many hands a TAG is going to call a button raise with that have a 2 in them - even if he thinks you're raising with a wide range. AK would tend to reraise, obviously, so we can't be overly concerned about that.
We obviously can't fold because villain is so unlikely to be ahead of us. We can't raise because raising has no value attached to it unless villain has something like KJ which he is willing to continue with. We call and let him take a stab at the turn if he wants, there's little danger in letting him see another card as not a lot of turn cards scare us. The call of his flop raise may well scare him into check-folding, but I think it's the best thing we can do.