Does your backup use WITH INIT? It really sounds like the backup is stacking up. What is the precise command you're using to do the backup. If you're using the GUI, script the command out using the button on the top of the window.

Also, is your database in FULL recovery? If so, are you running log backups? You need to if the database is in FULL recovery.

I've never seen a full backup multiply the size of the database. It's only going to backup the pages of the data files themselves (usually smaller than the database) and the pages of the transaction log. For it to suddenly take what should only be close to 2gb and turn it into 32gb, something else that you're not telling us is occurring.