Short HU session vs v.good player

[slik]

Q9o hand (below). you 3 bet preflop and autobet flop. would follow through on turn be +EV, or were you afraid of getting bluff raised? or was that a whiffed CR attempt? cause it just seems that by checking the turn you've given up on the hand.

Preflop: Hero is Big blind with 9s, Qd.
Button (poster) raises, Hero raises, Button (poster) calls

Flop: (7.00 SB) Jh, 7h, 4d (2 players)
Hero bets, Button (poster) calls

Turn: (4.50 BB) 2h (2 players)
Hero checks, Button (poster) checks

River: (4.50 BB) 7d (2 players)
Hero checks, Button (poster) checks

Final Pot: $599

Results in white below:
Button (poster) has Ad 8s (One pair, sevens(ace kicker))
Big blind has 9s Qd (One pair, sevens)
Outcome: Button (poster) wins $599