$25 NLHE Full Ring: SB 3bet bluff goes wrong, I am confused by the action

pokerstars Zoom No-Limit Hold'em, $0.25 BB (9 handed)

Button ($28.14)
Hero (SB) ($28.68)
BB ($12.50)
UTG ($6.04)
UTG+1 ($20.28)
MP1 ($31.34)
MP2 ($12.26)
MP3 ($29.09)
CO ($12.84)

Preflop: Hero is SB with Q , 10
6 folds, Button raises to $0.75, Hero raises to $2.50, 1 fold, Button calls $1.75

Flop: ($5.25) 3 , J , 10 (2 players)
Hero bets $2.35, Button calls $2.35

Turn: ($9.95) Q (2 players)
Hero checks, Button bets $23.29 (All-In), Hero folds

Total pot: $9.95 | Rake: $0.45

BTN is unknown but most people steal super wide and those who call 3bets tend to give up a lot of flops. I am also unknown to him and that means he should be careful here since most people don't 3bet wide from blinds.

BB is a TAG who sees me as tight player and he is unlikely to do much here without KK+ (he can't setmine since BTN might 4bet or shove).

I cbet flop a bit smallish but it usually works enough to make it OK. This time he calls and I am prepared to give up unless I bink the turn... which I kind of do with 2P but I am now behind flushes, AK (easily in a calling range for BTN if he hates stacking it off preflop), sets (likely calling hand on the flop) and even random QJs hands.

Soooo, the turn... I dislike betting here since a lot of his calling range likes the card so I check and expect to call any small enough bet to try and bink the full house.

He shoves pretty much instantly and now I am wondering what hand can he have? Only hand that shoves here is a small flush, right? This smells bluffy like hell but so many hands beat me I just can't call it profitably.

I prefer betting that turn and if he shoves depending on price, probably an easy fold.

Sure, but if he just calls turn again and I miss then I have no idea what to do on the river?
If I check there he can push me off the best hand (he can call turn with a flush draw and whiff it) and betting again achieves nothing.

The whole situation is pretty tricky it happens when you 3bet bluff

This is the problem with suited broadway cards to 3-bet bluff with: when they hit, the stronger 3-bet calling range of your opponent hits *harder*. AK/QQ/JJ/TT are all very happy with their hand.

Preflop is a hell of a delimma. I don't like 3-betting, since we know nothing about a full stacked guy, and our hand is dominated by his calling range. I don't like calling, since we set up the shorty to squeeze over us (since you say he has taggy stats). I don't really like nit-folding, but I'm kinda leaning towards that.

Flushes are such a tiny part of villain's range, forget about them on the turn. I think whatever you do, probably doesn't matter, as most choices are prolly close to 0 EV. But he could be shoving a lot of big heart draws or pair + heart draws here. So I probably call it off, but it really doesn't matter.

I am snap calling this, good check on the turn which induced a shove but the fold was pretty awful in my mind, whatever he had you just cannot laydown after playing the hand the way you just did till the turn. He could be shoving AJ, AQ, KK, AA and of course some hands which might have you beat obviously like a straight or flush but there is no way i am folding this as i think we have the best hand and even if we don't we still can improve on fifth street.

No matter what his stats are, no matter what kind of player he is - snap call.