When an aircraft requests 'deviation 20 miles right of track due to weather', what is the air traffic controller's responsibility before issuing the clearance?

1. Verify that the requested deviation does not conflict with other traffic or penetrate active restricted/prohibited airspace, approve the deviation with clear traffic parameters, and issue an instruction to report when back on cleared airway.
2. Deny all weather deviations regardless of storm severity.
3. Order the aircraft to shut down all engines.
4. Transfer the aircraft to visual flight rules immediately without pilot consent.