4NL - QQ overpair OOP

Button is 37/15 over 200 hands, folds to flop bet 60%.

Cake Poker No-Limit Hold'em, $0.04 BB (7 handed) - Cake-Poker Converter Tool from FlopTurnRiver.com

MP2 ($3.92)
CO ($4)
Button ($3.99)
SB ($4.25)
Hero (BB) ($3.96)
UTG ($4.57)
MP1 ($10.94)

Preflop: Hero is BB with Qhttp://www.flopturnriver.com/pokerfo...ilies/club.gif, Qhttp://www.flopturnriver.com/pokerfo...lies/spade.gif
4 folds, Button bets $0.08, 1 fold, Hero raises to $0.32, Button calls $0.24

Flop: ($0.66) 4http://www.flopturnriver.com/pokerfo...es/diamond.gif, 6http://www.flopturnriver.com/pokerfo...lies/heart.gif, 4http://www.flopturnriver.com/pokerfo...lies/heart.gif (2 players)
Hero bets $0.40, Button calls $0.40

Turn: ($1.46) 3http://www.flopturnriver.com/pokerfo...es/diamond.gif (2 players)
Hero ??

Bets again

bet $1.00, play for stacks.

bet bet shove

I like bet bet shove. But bet flop more, what does he call at 40c and fold at 50c?