Unfortunately It is not possible to adjust daily campaign budgets based on weather because campaign budgets are not at the geo level - they affect the campaign as a whole. Bids, on the other hand, can be manipulated independently for each geo location that you are targeting within your campaign.
One potential workaround for adjusting campaign budgets based on weather, is to set your campaign up in the following way:
Create a few ad groups in Facebook, or a few campaigns in AdWords with different daily budgets, all targeting the same market, and then set up rules in WeatherAds to activate/ deactivate them based on your desired weather. The effect would be similar. Here's an example setup for AdWords:
Campaign Daily Budget Geo Targets Weather targeting
Campaign 1 $50 California Only show ads when dry
Campaign 2 $100 California Only show ads when sunny
Campaign 3 $200 California Only show ads when hot and sunny