On a filesystem that supports hardlinks you can create multiple full backups that share their disk usage for files that have not been changed.
Assuming the backup disk is mounted on /backup
# remove the oldest backup
rm -rf /backup/root.1
# move the one-but-oldest backup to the place of the oldest
mv /backup/root.0 /backup/root.1
# copy the current backup using hardlinks
cp -al /backup/root /backup/root.0
# use rsync to update the new directory
rsync -ax --delete / /backup/root
echo "This backup was made on `date`"> /backup/root/stamp