I know this is a bit off topic, but I would probably talk about a weather station device which doesn’t need the internet. That’s what I use personally.
I explored Ocula in the past but it seems unmaintained? Plus it should be a PWA so there is no widget support.
If PWA or other web services are acceptable, then the observatories of different countries might also fit and could provide better result than solutions using OpenMetro. In this case just use a good web browser.
Is it necessary to have additional software on your device for checking the weather? Would a weblink on your Home screen (that opens in a private browser) not suffice?
The OP mentions checking the weather, not writing a dissertation. Simple webpages can look and work just as well as a dedicated apps (if not better than some offerings), and can be safer and more private too. What is the RL benefit of such software to warrant recommending people have another app on their device? Why not visit the website of your preferred source of weather forecasts (example: Florida - BBC Weather)?
I use QuickWeather. You can use this along side Open Mateo to meet all of OPs requirments. Both the app and and the weather api are open source, no account is required, and from my amateur reading of the privacy policies they both seem acceptable.
I don’t see a lot of other people that use this app but I have always really liked it.
It’s true that it can be relatively useful to use the web, I sometimes use DuckDuckGo “[Town] meteo” and it’s good. It has quite poor information though (no UV, no graphs, no millimeters of rain,…)
There is an open-source actively maintained weather app called WeatherMaster on Github released in June 2024 written mostly in Javascript that is “inspired by the Google Pixel weather app”. It however does not mention privacy as a characteristic of the app.
What do you think of it ?
I use Breezy for about 10 months now. One minor thing that I really like is the minimalist temperature display on the status bar at the right side of the hour. I don’t need a widget or to open the app to know the temperature:
This is a good idea because all weather apps require access to your location in some form in order to function.
For iOS, I think Hello Weather might be a good option as it’s privacy policy looks good and the app overall works well. Only problems I can think of is that it’s closed source and some more advanced features are paid. Otherwise, for iOS, the default weather app might suffice, although it definitely has its issues (for example, the radar on the default app is awful and struggles to load).
FWIW, I personally think the below would be the better option. Still, it varies between people; some could find x better while others prefer y, and a small minority likes z.
I suggest using the website of your local meteorological institute. It is completely unnecessary to download an entire app just for the weather. Besides, private weather sources often obtain their data from state sources anyway. Furthermore, they inherently lack a commercial interest in collecting your data, so their privacy policies are generally quite favourable.