iTunes stores iOS device backups in ~/Library/Application Support/MobileSync/Backup. Each folder within the Backup represents a different "backup" that will be presented as a possible restore source when restoring an iOS device.
In the process of restoring from a backup, iTunes migrates the data from one of those Backup folders into another, sibling folder, that will naturally end up being the same size.
Because you end up with two distinct backup folders, it follows that in order to restore an iOS device, you need to have at least as much free space on the device as the size of the backup subfolder. In my case it was more than 50 GB.
In order to restore my iPhone, I needed more than 50 GB free on the disk where iTunes finds my backups, so I copied the backups folder to another disk with lots of space, then made a symbolic link to it at the original location:
% cd ~/Library/Application Support/MobileSync
% cp -r Backup /Volumes/BigDisk/Backup
% mv Backup Backup-original
% ln -s /Volumes/BigDisk/Backup ./
(Replace the volume and folder names by those on your hard disk.)
Mac OS X Hints
http://hints.macworld.com/article.php?story=2012091401150782