Weather affects me if the overall climate isn't something that suits me well. Example: I lived in Minnesota for 9 years after college, and the intense winters and chronic lack of sunlight began taking a toll as the years went on.
It was one reason when I moved, I was very excited to be moving to a location that had the greatest number of sunny days a year in the U.S., and milder winters; and I gotta say, after being here almost 3 years, my overall mood is noticeably improved compared to how it had become when in Minnesota. Of course there are other factors too, but weather is a component.
That said, if the 'baseline' climate is to my liking, then I definitely, absolutely love and appreciate daily changes / the seasons. I appreciate/like the cloudy and rainy days, and love living somewhere that actually has 4 seasons and temp changes. Sun is important to me though....