Another set value extraction hand (50NL)

Last one from me today, I promise! Opp's HUD stats were 24/8 over a very small sample size (25 hands). Does anybody just flat call the flop or do you re-raise every time?

PokerStars No-Limit Hold'em, $0.50 BB (9 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

MP1 ($77.35)
MP2 ($42.80)
MP3 ($50.30)
CO ($6.40)
Button ($72.80)
SB ($50.25)
BB ($46.05)
UTG ($29.25)
Hero ($50)

Preflop: Hero is UTG+1 with 4, 4.
1 fold, Hero raises to $2, 2 folds, MP3 calls $2, 1 fold, Button calls $2, 2 folds.

Flop: ($6.75) 3, 4, 7 (3 players)
Hero bets $4, MP3 folds, Button raises to $10, Hero raises to $20

This is quite an interesting hand for me. Please flame my bad habits: here they are

Dry board, pf raise and cbet, button looks like he is testing you (the old "i put him on AK" syndrome). Flat call and a check will probably lead him to bet into your weakness on the turn, where i would push over.

Is my thinking bad?

Caveat, I never played full-ring.

I'm thinking the 2.5x raise is either 77, 33, 56, or 99-JJ. He bets the turn with the first 3, checks behind with the last 3. Any JJ+ on the turn kills our action from most of his range we beat. I mimic his 2.5x raise and make it $25, then push the turn.

Ginger, I think villain checks behind turn a lot. Our hand is too good to bluff catch, so let's put him to a tough decision. Also, what other hands would you call and check-raise with?