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.

AccuWeather for the "hyper local" weather.

Geometric Weather from FDroid is my absolute favourite. Clean, no adds. It even has a live wallpaper that shows current weather which I love.

I use Weawow, I like their widget and how customizable it is.

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.

I always like wunderground for its accuracy and there use to be an app for it, but HP cut off the API. Now I use Prognoza on f-droid, seems OK.

I just started using weawow. So far it's pretty good.

Radar Scope so I can see where the rain is headed.

I also have like seven other weather apps that never agree with each other exactly, so I just see what the consensus is amongst them all and guess.

Yr Weather https://play.google.com/store/apps/details?id=no.nrk.yr

Seems to be the most representative of my specific location.

Shadow Weather (https://play.google.com/store/apps/details?id=com.noaimgames.shadowweather) has a great presentation of detailed weather data, multiple weather services to choose from, current and future radar, and good developer support.

Flowx

Meteoblue

I just do a Google search when I need weather info, never felt the need for an app

The built in iOS app.