The weather app YoWindow is a very visual weather app, making it work very well on Android TV. It is “a living landscape that reflects your actual weather. For instance, if it’s raining – it rains in YoWindow.”
The app requests your location and then uses that to present a nice visual window that is based on your actual time and weather. A stats overlay provides some more precise information about the weather.
It’s a very nice app that can be displayed in the background, and it supports being a screen saver.
The app is free to download on Google Play. There’s also a paid version.