0,1/0,2 Jj

I definitely think that call down with JJ is the right play without reads and even if we are sure he has Ax. i think its correct to call the raise and river is rather blank so yeah.

IF you have the read on a passive guy you should fold because this check/call checkraise is the common valueline from fishy opponents. There is no draw possible. You think he's checkraising 8x or a purebluff? If he's passive he does have Trips almost always and JJ just becomes a bluffcatcher. Against unknown or with just a vague read i would call down as well.

He made a few moves which gived me a healthy suggestions he is weaker passive player, but still, i didnt had at that point any good certain reads.

If im not sure about how he reacts on such boards or such Turns we can justify colddown with JJ for note or there is a still fold?

Lets roughly figure that your opponent need a success rate for his bluff of 33~. Pot ist 4,5BB und he's got to put in 2 more. he would win 6,5BB if the bluff succeeds. If you even fold JJ and just continue with Trips, you fold way more than just 33% of the time and he's winning. But that's just the theoretical approach. Without a read i would call it down and make a note. There should be no reasonable worse hand he's checkraising with in that situation but if he's not aware of it, you may be still ahead.