Villains first hand at the table, so no reads. Checkbomb a good idea?

PokerStars No-Limit Hold'em, $0.25 BB (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

Button ($16.75)
Hero ($39.45)
BB ($25)
UTG ($6.50)
MP ($2.35)
CO ($40.65)

Preflop: Hero is SB with K, K.
1 fold, MP calls $0.25, CO calls $0.25, Button calls $0.25, Hero raises to $2.5, BB calls $2.25, MP folds, CO folds, Button folds.

Flop: ($5.75) 4, 7, 4 (2 players)
Hero bets $4.5, BB calls $4.50.

Turn: ($14.75) Q (2 players)
Hero checks, BB bets $10, Hero raises to $32.45 (covers villain who has about $8 left.)