What is an example graduate admission grading system? How much is GPA weighted? It is said in a variety of sources that the graduate admission committee uses a grading system. For example, if the total score is 10, the adcomm will assign 6 points to research and recommendation, 2 points to GRE, and 2 points to GPA. It is also heard that GPA is only used for the initial screen because different school grades differently.

So my question is, where I can find an example grading scheme? i.e. How much is GPA, GRE, research, and recommendation weighted? I need to know what is the best thing to work on for the grad admission.
Don't bother looking for a magic formula. Everything that is considered by the committee matters, and it's unlikely that you'll ever find someone who will tell you explicitly a specific cutoff for GPA or GRE that will get you in, because you could have a high GPA but lousy letters of recommendation or vice versa, and neither case will likely result in admission.

Moreover, many schools will not operate on such a system, particularly in smaller departments that do not have huge numbers of applicants. I know that I've never used such a system at any of the institutions I've worked at.

So the best advice, trite as it is, is to try to work on everything. It's more important to find someone who's willing to champion your application in the admissions committee than try to "check boxes." You never know what it is that will get you in—perhaps someone's letter of recommendation resonates because he or she was a classmate or personal friend of someone on the committee, or perhaps you expressed an interest in your personal statement that attracted the attention of someone looking for a new graduate student. (And, of course, a high GPA never really hurts.)