I think I learned something today... Deep stacked with KK

Both fish: 3bet/calls ship KQs, 4bet/ship KQs, 4bet ships A5s & 

I know I've been blogging about deep-stacked poker lately, and chastising my opponents for deep-stacked shoves / poor play.  I think turnabout is only fair play; I get caught in a deep-stacked trap.  I have reasons, which I'll share, but I still think I can get away from the hand & don't.  I learned from it.

We're at the $0.25/0.50 tables - my usual stomping grounds as of late.  I've been starting to play up to the $100NL tables, but the traffic is so infrequent, the volume is somewhat meaningless.  Anyway, I'm sitting on $140, but my largest stacked opponent has $93.61.

Folds to UTG+! who opens for $3 - larger than a usual raise (typical for these stakes is 2.5-3x.  A player calls to my right and I look down at KK from the CO.  Because of the large open and flat, I 3bet to $12.75 - this pot is getting larger, quick, if I get even one caller.  SB 4bets to $40(?) with $53.86 behind & original raiser shoves his $61 stack in.  Notes on the 4better are: "3bet/calls ship KQs, 4bet/ship KQs, 4bet ships A5s" and shover are: "O/c large 3bet K9o."  These are both labeled and noted as fish.  That said, I don't have any notes on a LARGE 4bet so deep-stacked, but these players can overvalue JJ,QQ, AK here.

Thoughts on my action?  Can I reasonably fold KK here?  Ever?  Against the shipper, I don't think I can, or should ever fold KK.  That's for ~100BB, though.  For ~200BB, does the calculous change?  I'm staring down a 80BB 4bet, who doesn't look like he's messing around.  I don't know; am I stuck in the matrix here?

Short of it is: I shipped my $141.22 only to get snapped off by my second deeper-stacked opponent.  I'm up against AA & AA.  Am I making a mountain out of a mole hill?  I think my lesson learned is even I blind squirrel finds a nut every so often.  Respect a 4bet and even respect a fish!

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The hand in question is linked here.