folding KK on a raggedy board to a lot of aggression

[jfk]

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Very bad. As you noted, even if you are 100% that he has 77 or AA, you must peel to try to hit a set. And can you really know he never does this with QQ/JJ (perhaps planning to take a "free" showdown if you call down)?

And you really need a killer read to fold KK HU on a dry board.

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From your description of his betting habits you can't fold here. If you intended to fold to a cap then there's little purpose in putting in that third flop bet.

This guy could have any pocket pair here, from the middle up. You could trail a set of sevens or pocket aces but you lead against the majority of his range. Even AK or AQ could be played this way (especially if he has reason to believe that you'd throw away anything but the mortal nuts here).

You have to call down here. This is a very big pot and you may be ahead. If he has aces, bully for him.