Solution 
Ok. I think I have found the root of the problem. And it is not related to the server at all. I am using LibreWolf as my browser. So because it has very strict security policy and low memory usage, it does not cache files larger than 50kb.
I went to its settings about:config and filtered variables browser.cache and found it out.
After I changed those settings, those LARGE js files started being cached, and the web site works smoothly now.
Thanks everyone for any help and support. 