200NL: missed AK on 3bet pot against short stack

$1/$2 No Limit Holdem
10 players
Converted at weaktight.com

Stacks:
UTG Bhagwan22 ($41.00)
UTG+1 AAfriko ($113.87)
UTG+2 Volcanow ($555.31)
MP1 TUDDYSTEEL ($130.87)
MP2 SoziD ($56.70)
MP3 Blaulicht ($112.46)
CO Raiba222 ($197.00)
BTN MrSantiago ($207.20)
SB danielneg111 ($114.13)
BB Hero ($263.65)

Pre-flop: ($3, 10 players) Hero is BB :ad: :kc:
3 folds, TUDDYSTEEL calls $2, 1 fold, Blaulicht raises to $10, 3 folds, Hero raises to $37, TUDDYSTEEL folds, Blaulicht calls $27

Flop: :jh: :5h: :jd: ($77, 2 players)
Hero checks, Blaulicht checks

Turn: :9d: ($77, 2 players)
Hero ???

villain was 21/13/3 and folds only 31% to 3bets.
My intention with the 3bet was to shove any FLOP, however, this FLOP frooze me.
Should this be a shove anyway? What about turn? c/f?

hmmmm stack sizes are really awkward here. I probs just bet 65/call push as I think that looks scarier than a shove. I dunno if it's too weak to just give up on the flop though.

I like the overshove on the flop, AQ might call us and otherwise it gives us max Fold equity.

That and people do stupid things a lot in this situation.

just bet big on the flop and call a shove, u don't have to shove it, and u are definitely tied to the pot with these stacks and the fact that he seems to be a huge donk

although, i highly doubt he ACTUALLY calls 63% ofyour 3-bets, that seems like a stat that you probably have a very poor sample on.

This is probably my least favorite spot to be in, it's also a very common one.

Just by thinking about it for a few minutes here, I think the best play is to bet the pot. You'll have max FE (as mentioned earlier). My concern is with calling the push. Are we getting good enough pot odds to call with AK?

yeah we'd be getting like eight to one