Disable Google Now weather notifications only

Go into the Google Now app and tap the three dots in the top-right corner of one of the weather cards. You'll get a pop-up that reads "Interested in weather updates for your location?" Tap "NO" and that should be it.

If that doesn't do it, go into the Google Calendar app, open the menu, and select "Calendars to Display." If the local weather is included in that list, uncheck the box next to it.

On Android I finally figured out how to only disable the weather notification, without removing the weather card or disabling notifications in general.

• Open Google Now
• Open Menu (swipe from left or press ≡) / Open Settings
• Open Now Cards and scroll down to Get Notifications for sections
• Uncheck Weather or Sport or whatever you don't want to get notified about

You will still see the card in Google Now, but the notification is gone. Exactly what I wanted to achieve.