Great thread Max. I appreciate the time you put into this thread.
Here is my HH for the Q & A:

I've run into this situation a few times lately, where the turn bet/raise is either going to commit us or I can just shove. I don't want to fold out worse hands with an overbet, but I hate calling a river where I'm likely beat.

Unfortunately I don't have a great read here since I'm fairly new to the table. My image must be TAG and I'm playing tight. The villain here is loose and aggressive, probably about 50/15, aggressive but not a maniac post flop. He likes to call in position with any 2 suited or connecting cards.
On the turn do you push him all in or raise a callable amount with the intention to get it all in on the river regardless?
Note: With a high set, I'll sometimes slow play into an uncoordinated board(Please do not make this the emphasis of your critque unless it would help the hand dramatically).

PokerStars No-Limit Hold'em, $0.10 BB (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

BB ($7.85)
UTG ($27.45)
MP ($8.90)
Hero ($10.40)
Button ($9.30)
SB ($9.75)

Preflop: Hero is CO with Q, Q.
UTG calls $0.10, 1 fold, Hero raises to $0.5, Button calls $0.50, 2 folds, UTG calls $0.40.

Flop: ($1.65) 3, Q, 7 (3 players)
UTG checks, Hero checks, Button bets $1, UTG folds, Hero calls $1.

Turn: ($3.65) J (2 players)
Hero checks, Button bets $1.5, Hero raises to $5, Button calls $3.50.

River: ($13.65) T (2 players)
Hero bets $3.9 (All-In), Button calls $2.80 (All-In).

Final Pot: $20.35