Flop Decision 3bet Pot 50 NL: Shove/Call/Fold ?

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Flop Decision 3bet Pot 50 NL: Shove/Call/Fold ?

BB: $188.05 (Hero)
BN: $50
SB: $54.42
Preflop ($0.75) (3 Players)
Hero was dealt A A
BN raises to $1, SB folds, Hero raises to $3.50, BN calls $2.50
Flop ($7.75) 8 T K (2 Players)
Hero bets $4.60, BN raises to $14, Hero raises to $184.55, and is all in

Villain plays vp 24/pr 17/3b 9. FCB 25 and Raise flop cbet 13%. Sample is over 300 hands. 

I think he's fairly polar when he raises, but given fe and dead money in the pot I still think it's +ev to shove here even though I expect to be behind (aprox 35% equity vs combo draws, 2 pair, sets and the occassional KQ, if he has that in his raising range, I'm not sure) when he calls, so shoving has to be better than folding, right?

If I call here, I'm not sure how to continue on various turns and rivers, a bit lost in these spots, feels like when I call oop on a wet board I either end up w a bluff catcher by the river or villain gets to realize a lot of equity when I check, so would like to hear what you think abt this. 

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