The hand you're specifically afraid of here is AA with the NFD because you block 99 and you can fairly discount hands that have 66 and 44 as hands that he'd 3 bet preflop.  You're roughly a 70/30 dog to that hand specifically.  His line does look super strong, you're right.  As far as a range goes, if you include all the middle rundowns in a range of hands that might 3 bet prefop and then c/r a flop like this, you're about 59/41.  Still, in looking at this board and looking at your hand it's hard to conceive of you having both the worst made hand and the worst draw so I wouldn't fault you at all for just stacking here.  It's really going to depend if this villain is ever happy to get it in with something a little closer, a hand like AA78.

In the heat of battle at 100bb deep or less, I think I tend to just stack here because our hand looks so good, but in looking at the action closely I'm not really sure. 

I think stacking off is easily the best play here and wouldn't think twice about it. Your hand is way to strong to consider folding obviously and don't see much merit in flatting his raise. If you run into AA w/NFD then so be it.

Folding would be too nitty even for me.

I can't see ever folding it but I think it's actually a closer spot than it appears.  Would love for one of those math wizards to chime in here with a 50 line post :)

I might also stack off here but I wouldn't be very excited about it.  You're probably essentially flipping against his range assuming he does c/r somewhat wide here.  It pretty much depends on whether he stacks off with rundowns w/o flush draw, or something like AA78 like bogglor suggested.  If he doesn't have those types of hands, then you're either flipping or pretty far behind, and that's rarely a happy place.

I can't really see how you can fold though, and I seem to always suggest folding on these forums, so you probably have a super clear stackoff  ;-)

I guess the argument for folding would be that c/r after 3-bet is very often a strong hand, and it's pretty unlikely that you'll be happy to see whatever he shows you.