I dont think, this is a nightmare spot, and if you think about it like that, its probably because of tainted memory. First off all UTG can not profitably setmine with a baby pair here, so if he in fact did, then he made a mistake preflop. Not a big one but a mistake none the less. And he will miss his set 7 out of 8 times, so on the flop he is way more likely to have 77-QQ than a set.
Which is also why your flop size is totally fine. You want to get a call out of all those pocket pairs, and if you bet to large, they just fold. A larger size would have been better against the fish, but it did not really matter, since he folded anyway, and if fish had called and reg folded, you could have put the hammer down on the turn.
Checking turn is also fine, and when he bet, I am not loving it, but no you can not fold. You could just check-call though and see, what happen on the river. I am not sure, I love the check-jam all that much, because I think, he mostly fold all the hands, you are beating.
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