No history on the villain. Did I play the flop and the turn correctly?

Thanks.

Is there a reason to leave 0.38 for river call?
My initial idea was fold flop on such a dry board and 3way, often good. And I would bet flop with lower size.

No to the amount on the river call!
The only hand that made sense to my c bet i thought was Kx. On such a dry board i considered a set would have called and waited for another bet. Is this a bad assumption?
Thanks

He could/should call sets. The more he should call Kx.
The problem with this flop is we rarely see raise with gutshot and almost entire raising range beats 1pair then.

Yes. That makes sense. Thank you

In theory, on such a dry board, your Cbet sizing should be much smaller. Like 1/2pot or less, but at these stakes it's probably fine to bet bigger here. I prefer just calling the turn and probably x/c on the river as well unless you have a read on the villain. It feels kinda weak to bluff catch with top two pair but villain is really only repping sets with the flop raise because the board is so dry.

A little smaller OTF (but it's 2NL so going exploitatively large with value hands works for me too), and I'm c/shoving turn.

you got luck here. in the future, ill recommend you reraise him for info. if he have kq he can call you, and you check the turn, and he check the turn too because he will do pot control and go to SD.
on the flop vs your raise, if he does raise you, you are behind. easy game.

of couse he can raraise you for bluff, but while you dont have info, fold will be better game.

ps i dont rec do call here as you lose your initiative. You let him see free card, and bluff you.

Im not trolling, and Im not trying to be disrepectful. All readers need to avoid this line of thinking. Using terms like GTO, balance 1/3pot 1/2pot in NL2 will make you a marginal winner at best. You should bet as much as you can. I find my self shoving rivers on pot of $0.06 and get call by second best or worst hand such as TP, 2pair and some other wierd holdings. Dont try to be balance against an unbalance pool players.

Back to the OP question: I rather call down instead of going over the top. I will keep my eye on cards like 3,5,9. Chances of getting a fun(fish) player to raise with 2pair or better on the flop are very slim. They like wait until the turn or the river.