A fan-made hack for Scarlet Weather Rhapsody version 1.02 was created to disable the effects of weather.
Download it here and put it in your Scarlet Weather Rhapsody folder. It's a launcher application, so first make sure SWR is not already running and then start it up.
A very simple hack, it does not remove weather itself, but rather it just disables the effects caused by weather changes.
Both players must be using the mod in order for it to not desync matches.