Top set with QQ against check/raise

How am I going to extract the most here? Seems pretty clear opp has a drawing hand. I dont have any reads


Party Poker No-Limit Hold'em, $ BB (10 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

SB ($30.59)
BB ($61.31)
UTG ($64.55)
UTG+1 ($68.20)
UTG+2 ($49.25)
Hero ($49.70)
MP2 ($26.07)
MP3 ($56.50)
CO ($34.23)
Button ($14.68)

Preflop: Hero is MP1 with Q, Q. SB posts a blind of $0.25.
3 folds, Hero raises to $2, 5 folds, BB calls $1.50.

Flop: ($4.25) 4, Q, J (2 players)
BB checks, Hero bets $2.5, BB raises to $6 Hero ...

I re-raise to $20. You might lose him, but I think the board is too scary to just call here. Villain could have QJ or 44 too.

I'd make it $15 before I made it $20. You'd be giving him 2.8:1 on the call, which puts him in a bad spot, but if he likes his hand he calls.