Thank you!
There is another discussion on this issue in the Windows / Windows 8.1 forum.
I have copied some of the information below in case it may be helpful to others.
It seems many people are having the same problem.
MSN Weather app won't start - Microsoft server issue http://answers.microsoft.com/en-us/profile/4f4bbe20-4f78-4ffe-9551-3950a3baf034
Petr Vones asked on
Since 09/28/2015 the Windows 8.1 MSN Weather app won't start anymore. It is stuck at start screen with throbber, no errors in Event Log. It happens on multiple different devices simultaneously with multiple different Microsoft accounts. I have also tried different Internet connection.
It looks like a Microsoft server-side issue that breaks Windows 8.1 compatibility only. There is no fix yet, reinstalling does not help. It works for the first time only but breaks again after you close it and start it.
UPDATE 10/03/2015 - There is workaround that works for some users only: delete single .sqlite file in C:\Users<YourUser>\AppData\Local\Packages\Microsoft.BingWeather_8wekyb3d8bbwe\LocalState\Configuration directory while the application is closed. Read the whole discussion for details.
Please report the issue via the Feedback option in charms bar of the MSN Weather application.
Microsoft still has to fix it !