I have found through some testing that an ownership permissions problem causes BackupWordPress to create huge archives. I also found that when a backup is sized larger than the php.ini memory limit the process crashes with a php memory error.
My server is running apache with user group and user name of the server apache:apache. The individual websites have their own names so files would normally be owned websitename:websitename with the exception of files uploaded or downloaded through the web interface. These files would be owned apache:apache.
In the process of moving some directories between servers the /wp-content/uploads directory was reowned by websitename:websitename and permissions of rw-r--r-- and rw-rw-rw-. Under this circumstance tar archives had several files of the same name in sub directories under /wp-content/uploads/etc-etc-etc.
The fix for both problems above was to change directory ownership to apache on /wp-content/uploads. I also changed the permissions to 666 on these files. My tar.gz went from 131 MB to 5 MB.
I don't think the plugin should care about this ownership as both apache owned and websitename owned files are valid to view in a browser.