The only workaround I found is to use an override volume and set it to global for each weather and store the weather sequence inside that override volume and use BP to control the user weight of each volume to simulate weather changes.
It does work but feels hacky, and I feel like there should be some way to set the sequence weight internally inside the Day Sequence actor. So my original question is to ask if people have a better way to implement a proper weather system in the Day Sequence plugin.