What is the timeframe of the report you are trying to run? If you look at AMP Setup -> the historical data retention values define how long date is kept in the database for a report to be run (Keep in mind the more data you keep, the more disk space the database takes up, so there's a performance trade off. Most customers keep a longer history of reports, while a shorter history of clients to account for this behavior, and export both as CSV and PDF to an external resource - this is set in the report definition). So if you are trying to re-run an older report, the data is most likely already aged out if you haven't made any adjustments.
If you go to Reports -> Report Definitions, edit each report definition that you want to receive via email weekly -> set report run schedule to weekly and email address to send to. Or generate new report definitions with the above options set.