Search for the total number of cases closed during weekends for a specific date range

1. Create a saved case search. Lists > Search > Saved Searches > New > Case.
2. Add the following under the Criteria:

Criteria:
Formula (Text) is not empty
Formula: Case WHEN to_char({closed},'D') NOT BETWEEN 2 AND 6 then 'T' END
Date created is within this fiscal year

Results:
Number | Summary Type: Count

3. Save and run the search.

This will show you the number of cases created on your specified date range from the criteria.