Quote Originally Posted by MasterAdmin View Post
солнце бьётся = the sun beams [the sun rays] (poetic style)

I think it's related to солнечный луч бъётся (the sun ray beams)
Not in this case, I am afraid. The weather is foggy and rainy. The sun is tired of trying to fight through the clouds and the fog (or tired of beating itself against the clouds, which adds up to more or less the same thing). That's the image I am getting.
Although, of course, you can never be sure with pop song lyrics...