I don't really like folding pre-flop, especially because this guy's hand and thus subsequent play should be relatively predictable. You have a marginal A-A-x-x, but certainly not the worst that it could be.

The flop play seems a little odd to me, but maybe I am missing something. You say that this guy is tight and put him on a hand range that includes K-K-x-x. Then, a K flops and you check raise him after deciding that he can only have A-A-x-x here? You really have to have a lot of faith in your read, as you committed 1/3 of your stack to a board that you can't call a reraise against.

Is Mr. Tighty bold enough to stick over half his stack in with a reraise into a leading pot bet by yourself with nothing but A-A-x-x on that rainbow board? Probably not. So, leading here probably wins a small pot with a marginal hand (a good thing) and prevents you from losing a big pot with a marginal hand (also a good thing).

Your check/raise wins a medium pot with a marginal hand (good thing) but loses a big pot with a marginal hand (a bad thing).