based on Cesium Js, a free alternative to Google Earth
Since the Google Earth API has been deprecated and not supported after 2016, Cesium can become a good alternatives.
This prototype is very simple, but it will be not difficult to implement a more complex application with the use of real data supplied by free/paied weather service.
For example, OpenWeatherMap provides current weather data (available in JSON, XML) for any location on Earth
http://pafavero.github.io/weather-forecast-cesium/