My intuition thinks this spot is underbluffed, how do you guys range villain here and can we exploit overfold? (If anyone has data would be really appreciated haha)

Yatahay Network - $0.25 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

Hero (BTN): 112.08 BB
SB: 234.08 BB
BB: 128.16 BB
UTG: 106.68 BB
MP: 121.4 BB
CO: 127.24 BB

SB posts SB 0.4 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.4 BB) Hero has Q Q

fold, MP raises to 2.8 BB, fold, Hero raises to 8.28 BB, SB calls 7.88 BB, fold, MP raises to 27.64 BB

Is MP tight or loose? Do you have any history with them?

I'm not sure it's good, but my line here entirely depends on these 2 elements, and it can be jam, call or fold (rarely). I'm also happy to read what better players than me say about this.

I doubt this is something else than AK, AA, KK. Let's assume I am right, then you have 40% equity.

There are 47 BB in the pot already.
If you shove villain always calls. With 40% of the boards, you end up with 235 BB (minus rake) in your stack. With 60% of the board, you end up with 0 BB in your stack. So, shoving is worth 94 BB. But it costs you 103 BB.

Also, I don't like calling that much because when the flop comes A high or K high you hate life but when it comes low you often don't stack AK. Their 4bet is quite meaty, the bigger their 4bet the more we are in push/fold territory.

Sometimes the fish in SB wakes up with AA, sometimes he calls the shove with 88, we can ignore them I would say.

In *my* NL25 pool people do not 3bet enough, to say nothing of light 4bets. I don't know in yours? Plus here even if MP is prone to 4bet, maybe they will hesitate fearing SB does a fishy thing. Plus I guess with AK sometimes they just think "oh f..k off" and 4bet shove instead of this, so it skews their range a bit away from AK and a bit closer to AA/KK.

I am weaktight and can always find a lot of arguments for folding

i fold most of the time

Seems ok to push, annoying thing is most regs will just jam AK in this spot.
If SB is some kind of big fish it's comfortable jam, if not it's quite close maybe folding is ok if you think AK plays as a jam.