To the OP, did you try disabling the weather app to see if that solves your problem? It's nice to have the weather constantly showing, but personally I only need to check it maybe once or twice a day. So I just use a different weather app and just open it whenever I want to check the weather. My s3 used to last me 12 hours max, but now it lasts me at least 25hours. I am rooted, removed lots of bloatwares, and have a few tweaks.
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