I use an iPhone at the moment, so I don't have direct experience with the Android version, but I very much like Yr. It is free, I think open-source (they at least have a github page), gives you a good amount of info (hourly, 3-day, and long-term forecasts, graphs of temperature, pressure, wind, and rain UV index, maybe a few other things), gathers basically no data about users, has no ads, and has a reasonably good UI. It's maintained by the Norwegian Meteorological Institute, so it probably works better in Norway - but I am in the US and it's honestly been fine for anything that doesn't need minute-by-minute updates (per their website it updates every 6 hours outside of Norway).

I'll hijack your question, cuz I have one too. A few days ago I was trying weather apps from F-Droid, but neither seem to support widgets?

Are there simply not there or is there something wrong with my phone or whatever? I've tried at least 5 that have been updated this year, but neither showed up in widgets. (I have a lot of widgets, incl. AF weather and Weawow.)

I've tried OmWeather (F-Droid) and Breezy Weather (Github), mainly searching for nice-looking and customizable widgets to use, and in that respect Breezy is my winner for now. I know that Forecastie is also another good one.

I use RadarWeather. It requires an OpenWeather API key. Omweather apparently is the same but doesn't require the API key. I use RadarWeather because it has a true radar screen for viewing rain location.

It isn't the prettiest but it does have widgets.