See this earlier (just!) post:
https://www-secure.symantec.com/connect/forums/we-want-know-backup-size-directory-wise-client
If you know when the backups are from you should be able to limit it to specific start/end times. At the very least it should give you a 'ball park' figure.
***EDIT***
Having thought about that, it would only be useful if you were restoring the
full amount that was backed up in that specific image, so probably no use (think I'm getting fixated on this command!). But if you told your UNIX admin the figure from this command, you should definitely have enough space