SH50 - AQ vs BU steal

Known players:
[tg]Position_Stack:hands/vp$ip/RaisePreflop/AF/WTS/ORL/BBvsSteal/W$SD;Hero$66,25:///////;BB$42,25:134/38/13/6.8/22/31/80/50;BU$47,95:575/25/20/2.5/26/35/58/46;[/tg]
0,25/0,5 No-Limit Hold'em (4 handed)
Hand recorder used for this poker hand: PokerStrategy.com Elephant 0.106 by www.pokerstrategy.com.

BU openraise = 42%
Fto3B = 80%
FCB = 61%
TCB = 33%

Preflop: Hero is SB with A♣, Q♣
CO folds, BU raises to $1,75, Hero calls $1,50, BB calls $1,25.

I thought he wouldn't call my 3b with a weaker hand so i called.
Should i still 3b because of the loose bb?

Flop: ($5,25) A♥, J♦, 7♠ (3 players)
Hero checks, BB checks, BU bets $3, Hero calls $3,00, BB folds.

Turn: ($11,25) A♠ (2 players)
Hero checks, BU checks.

Was not sure when i should take the initiative.
Just donking turn would generate too much foldequity.

River: ($11,25) 4♠ (2 players)
Hero bets $5,5, BU folds, Hero gets uncalled bet back.

Final Pot: $11,25