with no dynamic, no reads thats hes out of line or overplaying hands its pretty easy fold. Most people at nl10 flat JJ and even QQ and AK being in BB shoes in this spot, so when he 4 bets its just super super nutty. I wouldnt be too happy with KK either in your shoes, because people play very tight when it comes to spots like that and especially in nl10.

I like a call better especially with position.
And fwiw I'd flat AA and KK as well here.
Due to positional dynamics (BB is 4betting against two players in steal positions) I think he is wider than you give him credit for in this spot.
QQ makes formidable sets and decent straights some times as well.

Ok a fold is possible here, and probably safer / less high variance, but on the other hand I agree that since this is a very frequent situation (CO raise/BTN 3bet), I've seen players 4bet pretty wide in these spots, even at NL10. So I guess flatting.. and then fit or fold on flop ? what about on this particular flop ? bet/call with our gutshot BDFD ? Either way I'm not liking it at all. And folding preflop seems so weak.