Blinds: €2.00/€5.00 (8 Players)
BN: €750.00 (Villain)
SB: €400.00
BB: €2000.00 (Hero)
UTG: €X
UTG+1: €X
UTG+2: €X
MP: €300.00
CO: €X

Preflop
(€7.00) Hero is BB with Ts9c8s6c
MP cals, BN raises to €25.00, SB calls, Hero raises to €100.00, MP folds, BN raises to €330.00, SB Folds, Hero calls

Flop
(€690.00) 9s7s3h
Hero goes all-in (€420.00), BN calls

BN has AdAhQd4d, Hero has 85% equity, runs it twice & wins both.

So recently I've started taking this line and it seems to be quite profitable + the spot comes up reasonably often.
MP limp-folds a lot so he's not really a concern for this hand.
Villain is a more or less straight-foward player, no feasts of tricks or creativity, I'm assuming he's playing recreationally, rather loose-passive, not getting out of line, generally limps preflop too much, overvalues bottom of AAxx range, overvalues dangler hands like KQT5.
For a long time my line in this spot was to call a BN raise and play it out post-flop instead of 3-betting as we are out of position and our hand flops well enough.
I opted to 3-bet with this reasoning:
Best case (often what actually happens):
MP folds, BN is in a spot where he has to polarize his range, if he 4-bet his range is basically AAxx, if he just calls, his range is mostly KKxx, high-rundowns (frequently with danglers such as KQJ5, AKT3), occasionally AQQx.
Worst case: MP shoves and BN re-shoves, SB folds, we get it in a reasonably well 3-way flip (EV break-even, high variance)

if Villain just calls we take it post-flop and play from there. If Villain 4-bets we call and have a very profitable flop play:

• Shove any two pair, pair+gutshot, 3 card wrap, pair+flush draw with big equity edge
• Get it in slightly bad with single pair and no draw.
• Check-Fold flops where we don't have 3:1 odds - most of Axx flops, most of paired flops, flops that we miss completely (no pairs, no gutshots etc).

By cutting out the bottom of our stack-off range we actually get a sizeable EV edge. And Villain of course has to stack-off 100% of the time since we are ~0.5 SPR effective (0.6 in this hand).

The counterplays from villain's perspective against this play is to either widen the 4-bet range (which can end very badly for KKxx and AKxx hands), or to start calling the 3-bet with a big portion of AAxx range which kind of "feels" suboptimal (partly because it's inviting a 3-way pot) and most live players will never do. Would love to hear your thoughts on this!

P.s. Table is on agreement to treat SB-pre for a 5€ when it comes to potting calculations