There are many views on whether or not you should include weather forecasts for an internet radio station. Most people feel that since you're broadcasting to the world, a weather forecast will be not be relevant. This is true if you're are not catering to any local audience. If you're a station that has a concentration on a local area then, I feel that it's ok to include weather. Make sure it's short and doesn't disrupt the main program content. You can also include a general forecast for various parts of the country.
At Edgewater Gold Radio, we focus on being local to the Delaware beaches. We include weather forecasts from 8am til 5pm weekdays. We also include lots of brief local information. The key word is "brief." Since our stream goes world wide, we must not take away from the main thrust of our programming which is the music.
If you're a music oriented station and are an internet only station, you can provide much more that just the music, just make it brief which can be a delicate balance to achieve.