Enable the console,set weather as you like :changeweather(WT_Clear)
This has been a thorn for a lot of players, but it's simply that Velen was intentionally very rainy. I've seen stretches where it rains for a week straight. I normally never get more than a day without rain. Usually, it's only 10-12 game hours before at least a sprinkle.
If your problem is not caused by a bug, just meditate a few hours and see if the rain has stopped. I understand your frustration with too much rain in Velen, but I'm sure it is intentional, due to the climate of that region. I make Geralt meditate during rainy hours and continue his journey once the sun is out again.
I know I'm late to the party here, but just fyi, you can always enable the console and use the command stoprain - I've used that command occasionally when I've run into the bug where you still see rain falling while you're inside a building.