Diagnosis
Yes. The battery is dying. The Spirit II E-310 uses a single AA lithium battery in the ignition module. Weak clicking is the classic low-battery symptom.
How to Fix It
Locate the ignition module box on the front panel, right of the control knobs. Push the tab and slide the cover off. Replace the old AA battery with a fresh one. Weber recommends a lithium AA for longer life, especially in cold weather. Reinstall the cover.
If That Didn't Work
If a new battery gives strong clicks but still no spark, the electrode wire may be detached or the electrode tip is corroded. Check the connection at the ignition module and where the electrode touches the burner.
Heads Up
Use a lithium AA. Alkaline batteries can leak and corrode the module terminals, destroying it.