Go to Today view, not Notifications and hit Edit at the bottom, make sure it is in the included list.
Also remember there is Apple default weather, now powered by The Weather Channel instead of Yahoo, then there is Yahoo Weather, and The Weather Channel app, just to name three. Both the default weather will appear in Today view if you want and you can also add Yahoo Weather which does so with a picture by enabling access per above posts with location services then editing the Today view. The Weather Channel standalone app does not have a Today view widget.