AT - how to play the unknown?

I literally sat down in the BB, so this is 2nd hand. How's my line. Too passive, or, given the unknown and the possible flush and straight (and maybe AJ, but I doubt it) potential am I just looking for an uber cheap showdown?

Poker Stars
No Limit Holdem Ring game
Blinds: $0.10/$0.25
7 players

Pre-flop: (7 players) Hero is SB with A:spade: T:diamond:
UTG folds, UTG+1 calls, MP1 calls, CO folds, Button calls, Hero calls, BB checks.

Flop: A :diamond: 2 :diamond: J :diamond: ($1.25, 5 players)
Hero checks, BB checks, UTG+1 bets $0.5, MP1 folds, Button calls, Hero calls, BB folds.

Turn: T :club: ($2.75, 3 players)
Hero checks, UTG+1 bets $0.75, Button folds, Hero calls.

River: 6 :spade: ($4.25, 2 players)
Hero checks, UTG+1 bets $1, Hero calls.

Results:
Final pot: $6.25

I raise the turn to $3. He could have the straight or flush, but even if he does, you have four outs to the nuts and more outs to the third-nut flush. If he calls then I probably block bet the river for $3 or so, unless an A or T falls, then I value bet.