hi
The Turn is certainly quite close here. I would probably be more inclined to bet 77/TT as compared to QQ. When you have QQ, the likelihood of him having KJ/X:hX:h is much higher, as compared to AK/AJ/QX.
He's a fish, which should mean that his preflop range is extremely wide. He would then have plenty of QX (but you block them a lot with your 2 Qs), and plenty of suited trash as well. I think your decision to check the Turn is not all that bad, but let's take a deeper look.
I'm just going to assume that he flats 40% of hands preflop, excluding the top 3% of hands.
TT-22, AQs-A2s, K2s+, Q5s+, J8s+, T8s+, 97s+, 86s+, 75s+, 64s+, 54s, AQo-A2o, K8o+, Q8o+, J8o+, T8o+, 98o
Let's assume that he's only going to continue on the Turn against a bet from you with pair+draws (pair+1:h or pair+straight draw) or better.
Board: QcTh7hAh
Equity Win Tie
MP2 28.22% 28.22% 0.00% { TT, 77, 9d9h, 9h9s, 9h9c, 8d8h, 8h8s, 8h8c, AQs-ATs, A7s, KTs+, K7s, Q5s+, JTs, Kh9h, Jh9h, Kh8h, Jh8h, 9h8h, Kh6h, 8h6h, Kh5h, 6h5h, Kh4h, Kh3h, Kh2h, AQo-ATo, A7o, KTo+, Q8o+, JTo, T8o+, Kd9h, Kh9d, Kh9s, Kh9c, Ks9h, Kc9h, Jd9h, Jh9d, Jh9s, Jh9c, Js9h, Jc9h, Jd8h, Jh8d, Jh8s, Jh8c, Js8h, Jc8h, 9d8h, 9h8d, 9h8s, 9h8c, 9s8h, 9c8h }
MP3 71.78% 71.78% 0.00% { QdQs }
While getting raised would absolutely suck for you, I think it would often be a better idea just to go for value on the Turn right away, since plenty of weaker hands will call you still, especially those with a draw to go along with their pairs.
Q
Q
7
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