78s Flop ship it?

I see this in Equilab:

Board: 7♥8♥5♥
       Equity     Win     Tie
MP2    44.58%  42.62%   1.96% { TT+, A6s, AhKh, AhQh, AhJh, AhTh, AhKs, AhQs, AhJs, AhTs }
BB     55.42%  53.46%   1.96% { 8d7d }

So we're marginally ahead.

We bet:
 To get better hands to fold
 To get worse hands to call

I'm thinking that this x/r is a semi-bluff, but once opponent re-raises, we're down to 4 outs to a full house.
Against a 3x open from UTG, I would fold 87s pre, 2.5x gives you marginally better odds, but since I'm rather nitty, I think I'd still fold.

Villain is not saying he has overpair, two pair or set but that he has flush or maybe sometimes nut flush draw with flop 3bet. I think flop raise is somewhat reasonable versus small cbet though I would prefer just call. Mainly because this board can develop in many bad ways and I would not really want to bloat the pot especially out of position. When he 3bets we have easy fold. With set I would call and try to hit full house. Though even that is somewhat thin.

Folding preflop even with rake side would seem extremely nitty to me.

Thanks for your feedback.

It might not even be a board over pairs want to cbet that much but overpairs with heart want to call your raise and without are probably more likely to just fold this board.But depending on the stakes you cant really rule those hands out i mean villain is 3betting the flop with a flush which is pretty bad they should be calling your raise imo.So possibly your shove is ok but again depending a lot on player pool tendencies and villain tendencies and how they play those over pairs