Blocking an APP's Notifications is the incorrect thing to do, it is correct to turn off the specific Notification instead.
If you block the APP you lose all Notifications, there's "Current Weather" and "Weather alerts for substantial changes" - blocking will silence the APP completely, you might want to know if there's a hurricane coming.
In Oreo: Settings -> Apps -> Google -> Notifications.
Now choose both or either:
"Weather alerts for substantial changes"
Only block IF there's no Setting, once it's gone it's difficult to know what you are missing; you'd need to figure out how to unblock, monitor it, and be back in the same boat.