HAND REVIEW - Facing a preflop 3bet against a strong range

I'm unsure about this hand:
http://www.pokerhandreplays.com/view.php/id/6833725


I think the variables to note are:
- villain has 39bb, I have 45bb
- I raised UTG
- his 3bet sizing (4x)

- one thing I haven't considered is the utg+1 caller. I really have no idea what he's doing this with.
- I don't think villain's position matters at all here as he is doing this purely based on his cards. I highly doubt he'd be 3betting me light considering I raised UTG.

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I only have 128 hands on villain, I don't think that's enough to be looking at positional 3bet stats. However, his 3bet stat is 11%. That said, I don't think he is 3betting 11% against utg opens. His cbet stat is 6/9 (67%).

I put his range at JJ+, AQs+, AKo.  (Should I even include JJ in this range given that I have JJ?)

Against this range, I have 38% according to pokerstove. However there are more combinations of AK than any other hand in this range, so should the plan be to call flop and fold on AXX or KXX flops?

It feels pretty criminal to be folding JJ here preflop, but his range seems very nutted. Should I have perhaps folded the flop? I don't expect him to fold the flop after committing so much of his stack. So I guess the question is would he commit himself with AK on that flop?

My guess:

I'm thinking we should fold the flop. It feels like the combination of 3betting a utg open 4x and committing himself on the flop is a bit too strong for AK, so I'd be facing a JJ+ range which I obviously do very poorly against. Thoughts?

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Edit: After talking this hand over with a few friends, the general consensus seems to be:
1) this is a shitty spot
2) his range is super nutted, considering both my range and utg+1's is super strong.
3) JJ should probably be the bottom of our range for continuing this hand.