To remove just gnome-shell-extension-weather package itself from Debian 9 (Stretch) execute on terminal:
sudo apt-get remove gnome-shell-extension-weather
Uninstall gnome-shell-extension-weather and it's dependent packages
To remove the gnome-shell-extension-weather package and any other dependant package which are no longer needed from Debian Stretch.
sudo apt-get remove --auto-remove gnome-shell-extension-weather
If you also want to delete configuration and/or data files of gnome-shell-extension-weather from Debian Stretch then this will work:
sudo apt-get purge gnome-shell-extension-weather
To delete configuration and/or data files of gnome-shell-extension-weather and it's dependencies from Debian Stretch then execute:
sudo apt-get purge --auto-remove gnome-shell-extension-weather
More information about apt-get remove
Advanced Package Tool, or APT, is a free software user interface that works with core libraries to handle the installation and removal of software on Debian, Ubuntu and other Linux distributions. APT simplifies the process of managing software on Unix-like computer systems by automating the retrieval, configuration and installation of software packages, either from precompiled files or by compiling source code.
apt-get is the command-line tool for handling packages, and may be considered the user's "back-end" to other tools using the APT library.
apt-get remove is identical to install except that packages are removed instead of installed. Note that removing a package leaves its configuration files on the system. If a plus sign is appended to the package name (with no intervening space), the identified package will be installed instead of removed.
How to remove gnome-shell-extension-weather package from Debian 9 (Stretch)