OpenWeatherMap provides many kinds of weather maps including Precipitation, Clouds, Pressure, Temperature, Wind. You can connect them to mobile and web apps.
There are two endpoints for accessing weather layers.
The following endpoint is available for everyone. It requires the API key authentification.
This endpoint is only available for users who subscribed to Developer plan and higher. It also requires the API key authentification. The access is given only by the request.
There is also availability to customize weather layers by using the Map editor. Click the link to check out the guidance on how to use it.
'Displaying weather data with the Google Maps API and OpenWeatherMap' manual:
Another implementation of map based on Leaflet technology supports OWM's TileLayers and current city/station data. It is configurable with many options. For current city/station data the library supports refreshing the data in intervals, some types of client-side clustering (show only the station/city with the highest rank for a defined pixel square), custom image set (if you provide one), different languages ("en", "de", "ru", "fr", but translation is incomplete), minZoom and others.
Source and documentation (README.md) is available on GitHub https://github.com/buche/leaflet-openweathermap
Example of weather map: http://map.comlu.com/openweathermap/
Check out the use case of Scanex leaflet.