I cannot find a way to disable weather notifications from Google app. Every a few hours I get in the notifications list "How it is like outside" - temperature and clouds.
I searched all over the place and couldn't find a way to disable that.
Open the Google app and press the menu button.
Settings => Google Now (click to the left of the toggle) => Scroll down and toggle the weather off
These notifications are still there in Google app, however, they are now not limited to weather. For instance, I was also getting traffic notifications. There are other categories like news, stocks and restaurant suggestions.
The feature is now called "Discover notifications" and is located in Settings -> Notifications -> Discover. There is a middle-ground option called "Data Saver" which is designed to save network traffic, but also results in the notifications being shown less frequently, if you still want to see them sometimes.
When you get the notification hold your thumb on it for a few seconds. Two options will appear. Choose stop notifications.
If this is from the Google app and not from the Assistant: