Level 2 Bet Sizing

This is a blatant example of a guy who is thinking about my hand and what he wants me to do but not about what I will be thinking or what his hand will look like to me:

Full Tilt No-Limit Hold’em, $20.00 BB (5 handed) – Full-Tilt Converter Tool from FlopTurnRiver.com

MP ($670)
Hero (Button) ($5377)
SB ($2000)
BB ($2030)
UTG ($1813.50)

Preflop: Hero is Button with 7, 7
2 folds, Hero bets $50, 1 fold, BB raises to $185, Hero calls $135

Flop: ($380) 6, Q, 7 (2 players)
BB bets $240, Hero calls $240

Turn: ($860) 9 (2 players)
BB bets $480, Hero raises to $4952 (All-In), BB calls $1125 (All-In)

River: ($4070) J (2 players, 2 all-in)

Total pot: $4070 | Rake: $3

Results:
Hero had 7, 7 (three of a kind, sevens).
BB had A, A (one pair, Aces).
Outcome: Hero won $4067

This isn’t a spot where he’s likely to fire a second barrel on a pure bluff, so his range for betting turn is going to be semi-bluffs and value hands. With a value hand here, he chooses a bet size that presumably gives me room to shove draws of my own. Trouble is, it’s pretty obvious here that that’s what he’s trying to do, and therefore I should not shove my draws but rather just call with them and hope either to get there or river a good card to bluff. With his draws, I imagine he bets a lot more, making clear that he is pot committed so that I don’t have room to rebluff him with a draw when he’d rather I fold.