Calling 4bets, vs. a 4bet range of only AA, with high card hands, and especially with Kings, is never a good Idea.
However, in this specific example, you would have the odds to profitably call the 4bet, but it is staggeringly close (you have 33,98% on average vs. AAXX and you need 33%). These kind of super marginal spots just boost variance and you don’t have to take them in micro stakes. Play ABC and you will be just fine.
If you know for sure, villains 4bet range consists of more than AA, then calling is fine.
And yeah, as played, you have to go with it on this flop.

fold to the four bet

Agree with Voodoo32 and plolearnerguy on this one. If you were playing against a known tough opponent and/or population, then we need to continue with a call vs the CO 4B because he will be wider than just AA there, but generally in those types of games they have AA and that's about it. I have seen some AKKX and AKJTds types of hands before, but not often enough to think that we should consider that in spots like this.

Theoretically, you shouldn't be folding, but depending on the play of people in your games, I could see laying it down.

One important thing to consider is that while you're getting 2:1 immediate odds, there aren't many flops you'll be folding, so your true odds are much worse. (Or, if you plan on folding many flops, you're not realizing all of your equity)

Thank you guys, very helpful feedback.