I've been using WeatherBug for years. I've never noticed it being a particularly heavy drain on the cell phone battery.
In any case, there are plenty of "The 10 [or 8, or 12, or 15, or whatever] Best Weather Apps" articles to be found via a quick online search. Go read a few of them, decide which of the weather apps sound interesting, and download them to your phone. I'm sure you'll eventually find one which meets your needs, without unduly draining your phone's battery.