I had a similar problem after my iOS update (albeit now back in 2015). My backup wouldn’t complete, it showed up as 0 Kb, the next backup showed up as 0Kb and I didn’t get an option to delete my existing backup.
I turned backup off and whilst I didn’t then get an option to delete my previous backup, the previous backup (0 Kb) did disappear of its own accord. I was then able to turn backup back on, the 0 Kb backup did not reappear and I was able to start and complete a new backup.
Some have reported that after they turn back off, the previous backup (0 Kb) does not disappear or that if it does it reappears when backup is turned back on (although they are then able to make a new backup providing they have space).
It seems that in some case the 0Kb backup is corrupted data and does indeed take up space in the cloud and it doesn’t appear that this can be removed by the user, if this is what has happened in your case, contact Apple Support, (change country if necessary) they have been able to remove the corrupted data for some users. If this link doesn’t work for you, select ‘Support’ from the black menu at the top of the page and then choose ‘More Products’ on the page that appears.