$109 Rebay turbo, PokerStars, ATs

PokerStars - $100+$9|25/50 NL - Holdem - 8 players
Hand converted by PokerTracker 4

Hero (UTG+1): 2,920
MP: 2,830 (VPIP: 30.77, PFR: 23.08, 3Bet Preflop: 16.67, Hands: 13)
MP+1: 2,469 (VPIP: 15.38, PFR: 7.69, 3Bet Preflop: 0.00, Hands: 13)
CO: 3,676 (VPIP: 14.29, PFR: 3.70, 3Bet Preflop: 0.00, Hands: 28)
BTN: 2,820 (VPIP: 18.46, PFR: 13.79, 3Bet Preflop: 10.00, Hands: 66)
SB: 3,120 (VPIP: 7.69, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 13)
BB: 2,745 (VPIP: 15.38, PFR: 7.69, 3Bet Preflop: 0.00, Hands: 13)
UTG: 3,045 (VPIP: 8.33, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 13)

SB posts SB 25, BB posts BB 50

Pre Flop: (pot: 75) Hero has A♦ T♦

fold, Hero raises to 100, fold, fold, CO calls 100, fold, fold, BB calls 50

Flop: (325, 3 players) T♠ 3♦ 5♣
BB checks, Hero bets 130, fold, BB raises to 450, Hero calls 320

Turn: (1,225, 2 players) Q♣
BB bets 2,195 and is all-in, Hero calls 2,195

River: (5,615, 2 players) 4♦

Unknown. I cound't saw logic there so I called like a chips bank. How would you play the hand on the flop and on the turn and why ?