$2 NLHE Full Ring: $2 NLHE Full Ring: Nut flush draw on flop

Party Poker - $0.01/$0.02 No Limit Holdem (9 players)
Party Poker Hand Converter Tool from CardsChat.com

SB Hero: $2
BB: $5.58
UTG: $0.57
UTG+1: $2.14
MP: $0.75
MP+1: $2.04
MP+2: $1.92
CO: $2
BTN: $2

Pre-flop: ($0.03) Hero is SB and dealt
UTG calls $0.02, 5 folds, BTN calls $0.02, Hero raises to $0.08, BB calls $0.06, BTN folds

Flop: ($0.20) (2 players)
Hero bets $0.12, BB raises to $0.24, Hero calls $0.12

Turn: ($0.68) (2 players)
Hero bets $1.68 (All-in), BB calls $1.68

River: ($4.04) (2 players)

I just got stacked by villain and decide to play back at him again with this hand since it still beats alot of his range. I flop the nut flush and feel pretty good about my hand. I decide to play this hand a little stronger and villain calls.

The turn gives me an Ace, giving me TPGK and a draw to the nut flush by the river. I decide to shove the turn since I have good fold and showdown equity. My AT is probably good against villain's range and I still have 9 outs to the nut flush so about 20% to make the nuts on the river. I also pretty much expect villain to fold to my strength on the turn.

I raise more pre b/c of the limpers. Flop is good. I think when you shove the turn you kind of force him to only call with better. I would rather just make a normal sized bet, c/r all in or check/call depending on player type.

Raise way more pre. What's with the overset shove on the turn though? Why would you want fold equity when you're likely ahead of his range?