The ideal privacy respecting weather app would download and update a local copy of every location's weather, and any requests you made would never leave your own device. I'm not sure how realistic that is, but as long you trust the Karlsruhe Institute of Technology, the government they operate under, and that the data being sent to OpenWeather is non-identifying or that they too can be trusted with your data, then this is probably the closest we're going to get.