Welcome to Android Central! Does it actually say "appupdate.co" somewhere on the popup?
Chances are that you installed some adware alongside one of your other apps. Are you using a 3rd party weather app, or the Samsung one? If it's a 3rd party one, uninstall it, and see if the popups persist.
If they do, then try booting into Safe Mode, which prevents all 3rd party apps from starting up. Then open them one by one, until the popups recur. That should give you an idea of which app is responsible. Safe Mode instructions are at the bottom of this article:
Reset: Samsung Galaxy S 4 | T-Mobile Support