AJo SBvBTN 3betpreflop drawheavy board

PokerStars, Hold'em No Limit - $0.01/$0.02 - 6 players
Hand delivered by Upswing Poker

UTG: $2.93 (147 bb)
MP: $5.53 (277 bb)
CO: $4.07 (204 bb)
BU: $3.35 (168 bb)
SB (Hero): $2.31 (116 bb)
BB: $3.44 (172 bb)

Pre-Flop: ($0.03) Hero is SB with A♦ J♥
3 players fold, BTN raises to $0.06, Hero 3-bets to $0.24, 1 fold, BTN calls $0.18

Flop: ($0.50) T♣ 9♣ T♥ (2 players)
Hero bets $0.23, BTN calls $0.23

Turn: ($0.96) 4♣ (2 players)
Hero checks, BTN bets $0.47, SB (Hero) folds

Total pot: $0.96 (Rake: $0.03)
BU wins $0.93

It's an older hand.
AJo at SB is in my 3bet/fold range.
BTN defends.
On the flop, I don't like my c-bet now. I think it's too big. 1/3 would make the same work.
Maybe I don't need to c-bet at all with my hand.

Board: T♣9♣T♥
       Equity     Win     Tie
BU     44.36%  41.63%   2.73% { JJ-22, AQs-A2s, K9s+, Q9s+, J9s+, T8s+, 97s+, 87s, 76s, 65s, 54s, AQo-AJo, KJo+ }
SB     55.64%  52.92%   2.73% { 55+, A2s+, K9s+, Q9s+, J9s+, T8s+, 98s, 87s, 76s, AJo+, KQo }