Turn can be bigger. Not much, maybe $.25 or $.30. His folding range isn't going to change much based on size and you want to build this pot. I expect most of his continue range here is overpairs and sets and those hands will call a larger raise.

Never folding river. As played I make the call all day long. I can't really see you being worse than 42% equity and it is usually going to be 50%+. It is actually probably close to being a hand you can reraise all in with. Leery of making this play in micros due to some fish showing up with more combos of KJ than KJcc here. However, some fish might have and call off with some weird overpair trap and that would offset the weird straights. Probably best to just call river I guess.

I would bet turn. Though the Q is good for UTG's range, your hand is very strong, and you want to bet and build the pot yourself instead of relying on your opponent. If he has something like AQ, he might even raise you here.

If you check and he has some hand with moderate to weak SDV, like 88 or AK, he may check back the turn. But check-raising is ok once in a while, and protects your range as well. As mentioned above, you can raise a bit bigger.

On the river, don't fold a set. You only lose to KJ and he can have a lot of other hands.

Any reads?
At these stakes I would just go for value whenever I can so betting big on turn would be default. As played I´d prob make it a bit bigger on turn and then definately bigger on river, something like .45. Betting small on river is a huge mistake that probably cost you a ton of money imo.

Would bet turn and river a bit bigger but on the stakes played you will win the pot a bigger % of the time then you loose the pot with a set.
Of course you will run against an opponent now and then that beats you with KJ or QQ but that is poker variance.
If he has QQ def make a note that it is perhaps a trappy player as he checked back flop and be a bit more cautious against that kind of opponent.

The vill had KJo