Hi Shannon Magnuson,
Welcome to Microsoft Community.
Unfortunately, we are experiencing the exact same issue as you.
We are unable to sign into our Microsoft account in the MSN Weather app, it is always loading in a circle.
We noticed that the latest version of the app was released in July 2022.
Outdated application code is at the core of this phenomenon.
We have submitted feedback on this issue via the "Feedback" option available in the "Settings" of the MSN Weather app.
If convenient for you, you may also submit feedback on the MSN Weather application.
Thanks for your patience and understanding!
Best Regards,
Kyo - MSFT | Microsoft Community Technical Support