Bad beat, but did I play it right at least?

Yeah, he sucked out on me. Could I have laid this down at any point?

Party Poker No-Limit Hold'em, $ BB (10 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

Hero ($15.50)
Button ($43.15)
SB ($35.25)
BB ($25.70)
UTG ($5.45)
UTG+1 ($5.20)
UTG+2 ($21.65)
MP1 ($50.61)
MP2 ($47.65)
MP3 ($5.55)

Preflop: Hero is CO with A, A. SB posts a blind of $0.10.
2 folds, UTG+2 calls $0.25, MP1 raises to $1, 2 folds, Hero raises to $3, 2 folds, BB calls $2.75, UTG+2 folds, MP1 calls $2.

Flop: ($9.35) 9, 6, J (3 players)
BB checks, MP1 checks, Hero bets $7, BB calls $7, MP1 folds.

Turn: ($23.35) 4 (2 players)
BB checks, BB calls $5.50.

River: ($28.85) T (2 players)

Final Pot: $28.85

Results in white below:
BB has 7h 8h (straight, jack high).
Hero has Ac As (one pair, aces).
Outcome: BB wins $28.85.

Buyin for full man.

He is a 65:35 dog on the turn and you push AI for $5.50 more. So he has to call $5.50 to win $28.85, so he may have "sucked out" on you, but he made a +EV call on the turn, his flop play isnt so great.

Given your stack size I would probably just push that flop, with a full stack your play would be alright.

Buy in for full, and turn push/near pot bet is acceptable.