Resteal?

[raze720]

Ultimate Bet - No Limit Hold'em Cash Game - $0.25/$0.50 Blinds - 6 Players - (http://www.legopoker.com/hh)

SB: $56.70
BB: $37.75
UTG: $47.25
Hero (MP): $50.00
CO: $98.65
BTN: $99.35

Preflop: Hero is dealt Ah Kd (6 Players)
UTG folds, Hero raises to $1.75, 3 folds, BB calls $1.25

Flop: ($3.75) 6h 3h 2s (2 Players)
BB checks, Hero bets $3.00, BB calls $3.00

Turn: ($9.75) 6s (2 Players)
BB bets $6.50, Hero folds
Uncalled bet of $6.50 returned to BB

Pot Size: $9.75 ($0.45 Rake)

I decided to fold this, following orders to "not get tricky." Would it not be more profitable though to bump it up to $16 here? It seems very likely to me to be a lame bluff.