[5NL] Bet sizing on the flop here?

Villain is raising frequently on the button, but this was the first time he had called a 3bet from me. I have only been on the table for about 15 hands so I don't have much info, but he seems like a fairly solid player.


Full Tilt No-Limit Hold'em, $0.05 BB (5 handed) - Full Tilt Converter Tool from http://www.flopturnriver.com/

UTG ($6.61)
MP ($7.50)
Button ($5.73)
Hero (SB) ($5)
BB ($7.54)

Preflop: Hero is SB with J, Q
2 folds, Button raises to $0.15, Hero raises to $0.45, 1 fold, Button calls $0.30

Flop: ($0.95) J, 2, 4 (2 players)
Hero bets $0.50, Button calls $0.50

Is this sizing okay? At this point i'm putting him on Ax, or 77+, perhaps JT/KJ. I feel like the bet is on the small side.. would 2/3 the pot have be better? My reason for betting so small is that I don't want to move him off his hand, as I don't see his range connecting with this flop very often... but I wonder if i'm losing myself money in this spot by not going for a larger bet.