there’s plenty of people with this issue. Weather alerts keeps turning back off on my garmin 820. I have seem multiple threads where users are unhappy with getting way too. Any weather advisories. It’s like they don’t monitor their own forums!
I also cannot turn off my weather alerts. Drives me crazy. And the online documents are wrong as there is no weather app toggle on The connect app to turn off
Do you want to turn off weather alerts on the phone, or on your Garmin device?
If you mean notifications on the phone, then when it arrives, swipe down the status bar, then swipe the notification to the side, and tap the cogwheel to adjust the concerned notification settings or to stop it.
If you mean notifications on the Garmin device, then in Garmin Connect go to Menu » Setting » Notifications » App Notifications, and disable notification from any apps you do not wish to receive on the device (incl. the weather app).
Or did you mean the Storm alerts? If so, then when on the barometer screen of your watch, press the Menu button, enter the Barometer settings, search the Storm Alert option, and disable it.