A319 Captain reported the aircraft weather radar system failed during cruise as the flight started to encounter poor weather conditions. Flight crew diverted and made an overweight landing.

Narrative

Departed from ZZZ and was enroute to ZZZ1. Approximately 1 hour into the flight; some weather was begging to develop on our route. I turned on our weather radar and started to adjust it. I saw a critical display on my ND (Navigation Display). It was WR ANT (Weather Radar Antenna)! Looked in the QRH and the ECAM supplemental manual. The manuals did not address this situation. Called Dispatch and asked for a patch to Maintenance Control. Maintenance Control had me pull the radar circuit breaker; but was not successful in restoring the radar system. There were two heavy lines of thunder storms between us and ZZZ1. We would have to pick our way thru the storms. After discussion with Dispatch; they requested that I divert to ZZZ2. Our discussion also included that I would be overweight on landing. Again; after discussion; Dispatch wanted me to follow overweight landing procedures in the QRH and land overweight. From a safety point of view; I agreed with Dispatch that this was the safest action. We [advised ATC] and landed overweight in ZZZ2.The basic Airbus aircraft has very unreliable Radar. A lot of the DU (Display Unit) displays are so dim; you have a hard time seeing any actual convective activity on the displays. This is of course after adjusting the radar antenna.Suggestions: Radar check on the ground before flying into known areas of convective activity.