This app was mentioned in 5 comments, with an average of 1.60 upvotes
The Weather Network has an Android TV app, haven't used my Shield in about a year so I'm not sure if it still works but it was my goto screensaver on there. https://play.google.com/store/apps/details?id=com.pelmorex.WeatherEyeAndroid.tv&hl=en_CA
If you want a weather channel app, this one is pretty good. Does local stuff too. The level of integration is impressive with the local weather ticker.
https://play.google.com/store/apps/details?id=com.pelmorex.WeatherEyeAndroid.tv
if you install this "The Weather Network" TV app...https://play.google.com/store/apps/details?id=com.pelmorex.WeatherEyeAndroid.tv
the live channels will pop up on the home page