How much do research papers in arXiv count (for graduate applications)?
Having a paper that was not peer reviewed but is available from arXiv will help you just as much, and in exactly the same way, as having a paper that was not peer reviewed and is available from any other easily accessed online source. The main things that are important are that:


You have written a paper (according to some definition of "paper").
The paper can easily be accessed and looked at by anyone wishing to evaluate your strength as a grad school applicant.


Note that the value of such a paper to your admission prospects can actually be negative if it is clearly of very poor quality, shows delusional tendencies (e.g., a paper with the title "A simple proof of the Riemann Hypothesis"), or comes across as a dishonest attempt to create a false impression that you have done something important when clearly you haven't. Setting aside such obvious exceptions, an arXiv paper will probably have a positive, but in most cases not very large, value for your applications.