[NL10] AQs in 3bet pot OOP

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[NL10] AQs in 3bet pot OOP

Blinds: $0.05/$0.10 (5 Players) SB: $13.91
BB: $10.83 (Hero)
UTG: $11.04
CO: $32.88
BN: $11.37
Preflop ($0.15) Hero is BB with A Q
UTG raises to $0.25, CO folds, BN calls $0.25, SB folds, Hero raises to $1.15, UTG folds, BN calls $0.90
BN is reg 22/16 over 850hands. 3bet 5% overall (4% 3/69 on BN). F3bet 60%. AF2.
UTG is loose player 37/25, 65 hands tho.
I think AQs is standard squeeze here. I should have squeeze bigger.
Flop ($2.60) 3 J T
Hero checks, BN bets $1.21, Hero raises to $4.05, BN calls $2.84
OK so here how I approached this spot.
This board connect quite a bit BN's 3bet calling range but I think most of his range is made of draws/ pair+draws/2over+draws/GS/backdoors. His value range would be JJ/TT/AJ which we also have in our range.
In game I decided to go for a x/raise to deny his equity. I'd be x/raising QQ+/TT/ probably JJ too even if we do block TP and all of my combos draw as semi bluff.
I think x/raise is better than cbeting because even with let's say a 66%-75% pot size bet BN will realize is equity too easily just by being IP.
Plan was to shove on any river if called.
Turn ($10.70) 3 J T 8
Hero bets $5.63 and is all in, BN calls $5.63
Now I'm sure you guys see what I didn't anticipated.
By x/raising to this size I left myself with a shitty PSR to shove turn & I think I have no FE with this sizing.
On the other part, by x/raising smaller BN still have good odds to call.

So 2 questions here :
1-Are you guys ok with x/raising in this spot ? if not why ?
2-If yes what sizing should we use in this spot

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