The backup file contains all your songs. So if the backup has 6gb, your songs also need about 6gb. That makes 12gb. And if you imported them from iTunes you most likely need another 6gb for iTunes.
Generally you can save space by deleting the backup file on the iPad once you stored it safely on your computer. As long as you don't add new songs, you can create database only backups to store your edits. Together with the full backup you can quickly restore your setup.
It is also a good practice to create an iTunes backup of your full iPad. That will include ST3 with all songs and settings.