Villain is 30/5 over 40 hands. He's limp calling and minraising a lot

Is double barreling here bad? If we're checking, whats our action if he fires into us?

Full Tilt No-Limit Hold'em, $0.50 BB (8 handed) - Full Tilt Converter Tool from FlopTurnRiver.com

saw flop

Button ($50)
Hero (SB) ($50)
BB ($144.50)
UTG ($50)
UTG+1 ($50)
MP1 ($53.80)
MP2 ($89.95)
CO ($75.10)

Preflop: Hero is SB with A, Q
2 folds, MP1 calls $0.50, 3 folds, Hero bets $2.50, 1 fold, MP1 calls $2

Flop: ($5.50) 2, 3, 9 (2 players)
Hero bets $2.75, MP1 calls $2.75

Turn: ($11) 6 (2 players)
Hero bets $6.70, MP1 calls $6.70

River: ($24.40) 5 (2 players)
Hero checks, MP1 bets $13, Hero folds

Total pot: $24.40 | Rake: $1.20