If you want to be mildly terrified, do a search on which weather apps do NOT collect and sell your data. Hint: you won't find many.
They are notorious for gathering background data, including your location, obviously.
Unfortunately, most of the weather apps that claim to not sell your data are subscription based and fairly expensive.
I used to be a weather app nerd, but I'm also a privacy advocate, so these days I just use a bookmarked weather website.
I tend to use the Google built-in one (which is getting a revamp soon), but I also subscribe to Weather Channel. This is nice because if you subscribe on the web it gets rid of ads on all platforms - Android, iOS, and web. Sometimes there are issues where you have to log out and back in again, but it works.