The weather widget uses the Apple iOS 5 Weather widget.  It uses the settings from the weather app.  By default, the weather app uses your local location.   The location is update automatically.   However, to conserve battery usage, we have changed the widget to not poll the location each time Notification Center is shown.  Instead, it is updated no more than once every 12 hours (on display).

If you would like to update the location manually at any time, simply tap the weather area.

If you would like to set the location permanently, you can do so inside the iOS 5 Weather app.