So how would you extract the most from the villan?

I'm playing $1/$2 this past week at a casino and playing fairly tight. My opening range was about top 10% and any pocket pair. I'm in the cutoff at a 9 handed table and get dealt 10-10. 3 players limp in, I raise to $10, SB calls all others fold; $28 in the pot.

The SB is a LAG with better poker skills than me, and I put him on a range of 30%.

Flop comes 10-10-6h. Woo hoo, quads.

SB checks, I check. I don't want to chase him off the hand, and my table image is TAG. I'd prefer it look like I had medium pocket pair or some Broadway...anyway...

Turn 2c. SB checks, I check. I really wanted an ace to hit for the SB to bet into me. Oh well.

River is 9s. Finally the SB over bets the pot $50. I come over the top for $100. SB folds.

Would you have bet differently?