Thanks for reaching out to the Apple Support Communities. I understand you've had some trouble with the Weather Widget, and I have some information that may help.
Have a look at the settings listed below to make sure your weather widget is set up to receive updates.
Go to Settings > Privacy > Location Services > Weather and choose the setting that works for your situation.
Go to Settings > General > Background App Refresh > Background App Refresh: Wi-Fi & Mobile Data
Go to Settings > General > Background App Refresh > Weather: On
After trying these steps check the Weather app and see if it's updated, then check the widget.
If you run into any trouble, please reach out again.
Best Regards.