Most people does not worry much about the size of their site. Specially if they have large disk or storage. It is very important to monitor the size of your site specially if your site is very dynamic like social sites or you are upload large video files, music files and photos.
If you are using your server for web server, database, email and other services/systems, it is very important to minimize disk usage. In most cases higher IO affects your site performance. It sometimes create bottleneck which usually causing high wait percentage of your server processes.
To know the size of your site, you can login to your hosting panel using the “admin” user.
user > (webuser) > login as (webuser) > web
Site size is also important to backup system. Large sites requires more advanced backup system.