K9 two pairs facing check/shove on the turn

As I've said before I have no experience with NL 50, but what do the real experts think about re-raising the flop?
X/R a really dry flop is a pretty standard bluff spot

In fact, I think there is a "theorem" a check-raise on a dry board is almost always a bluff.
Couldn't find it though.

He does it twice though, so ...

Fold pre, as played check back: you haven't 3 street of value and you don't need to protection.

Has he all pp when open from UTG-MP? I think that I call with top two pair

agree with fold pre and check flop. i don't think we want to stab a lot this board given positions, should probably do so with a more polarized range of sets/backdoors.
as played, pretty sick. of course you don't beat a value range of sets and a very small weight of AK AA, but can't villain ever have a backdoor draw? i want to call this one.

You mention he does strange things. what for example? Do you have any notes on his x/r that you seen from him before?
K9s for me is a 3bet or fold preflop against UTG. having played, I would bet OTF as you did 1/2 but would fold to his raise. we have TP but I do not think it is enough for calling a x/r and another 4 €. You need to know what will you do ott if he leads? fold? call again?

The fact that he checked ott is one of those strange things that you mentioned and I would check back. we are not worried about the flush get there otr so I would check ott with intention of calling otr.

as played I would call ott his shove. he can have many miss draws. the only think beat us is sets since KK would be a raise pf. I prefer lose my stack against this strange player with my two pair and have him to place a note for my like "no bluff villain! calling x/r with only tp, calling x shove ott with two pair" rather than "bluff candidate! he folds to x/r very often"

After all that is my idea.

I agree with the comments, thanks. Especially about preflop and turn

surely he just has AA here usually?

I don`t think he`ll check AA