When you see the pop up move your mouse over it, it should show a gear icon for its settings. Select that and turn off the notification.
Or you may have enabled by mistake this program to display notifications in your browser.
In Chrome
Go to Google Browser settings and type "site settings" in the search box. Go into site settings and under the recent activity you will find
www.accuweather.com. Click into that website site setting and find the button for "Reset Permissions" Click the button for "Reset Permissions and that should set notifications back to ask or simply change the notifications to "block".
In Edge, go to the three dots found in the upper right. Click on it and select settings and then site permissions. Scroll down to the bottom under allow and remove the accuweather url.
It could be because Accuweather has been enabled in notifications in windows.
go into notifications! Settings > System > Notifications & actions > scroll down > click slider to off on anything you don't want notifications from .