That is not how it is supposed to look like after the update. This is how mine looks like after the update below. Corrigendum: Your post got me confused a little bit. Now I know you post the Weather not the People app that you inserted inline in your previous statement. It seems to be something that has to do with your connection. I'd advise you check your internet connection properly.
People still won't update and as for Weather goes, every single page (except maps) shows the same error. This has nothing to do with Internet connection.
Seriously, mine updated. Try to re-install them from Store not Store(beta) under Account - All apps. Don't forget to unpin them from the Start first. You can as well run this at elevated command prompt to see if it helped: Code: Get-AppxPackage | % { Add-AppxPackage -DisableDevelopmentMode -Register "$($_.InstallLocation)\AppxManifest.xml" -verbose }