A full backup needs as much space as your songs. So if you have one backup with 3.2gb then you most likely have songs with 3.2gb in the folder too. That sums up to 6.4gb.
Why not copy the existing backup to the computer. Then you can delete it from the iPad and create a new.
If you want to keep track of your lyrics edits and don't switch songs too often, keep one full backup and create database only backups often. Theoretically you only need to create a new full backup when you add or remove songs.