When should I fold an overpair?

I have no stats (Just PartPoker things...), but I know that SB is one of the toughest regulars I played with on the site.

PartyGaming - $0.05 NL (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

BB: 109 BB
UTG: 101.4 BB
MP: 201.6 BB
Hero (CO): 152.8 BB
BTN: 100 BB
SB: 138.8 BB

SB posts SB 0.4 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.4 BB) Hero has Q♥ Q♠

fold, MP raises to 4 BB, Hero raises to 14 BB, fold, SB raises to 33 BB, fold, fold, Hero calls 19 BB <- After a cold 4bet, I don't want to go broke with ~140bb effective stack, so i call. I think he would play like this with a very strong range, like QQ+, AKo and AKs

Flop: (71 BB, 2 players) 9♣ 7♣ 2♦
SB bets 25.6 BB, Hero calls 25.6 BB

Turn: (122.2 BB, 2 players) 7♠
SB bets 80.2 BB, Hero???

Am I right If I say, he has only QQ+ here? Could he play like this with JJ?

According to PT4, I need 28% here.

Against QQ+ I nearly drawing dead:

Board: 2♦9♣7♣ 7♠
       Equity     Win     Tie
CO      8.04%   4.20%   3.85% { QhQs }
SB     91.96%  88.11%   3.85% { QQ+ }

If he plays like this with JJ+:

Board: 2♦9♣7♣ 7♠
       Equity     Win     Tie
CO     35.65%  33.01%   2.63% { QhQs }
SB     64.35%  61.72%   2.63% { JJ+ }

Actually I like the fold better but what do you think? Close my eyes and call or fold?
If fold, should I folded earlier? (I didn't because OTF I thought he can still have AKo or AKs, too. Not sure if I am right)