I've had the same issue with being unable to delete a number of "0 Bytes" cookies on my iPad for a while, but recently an eBay.co.uk cookie of 508KB size began to exhibit the same behaviour - at which point I "snapped", enough is enough! I found a solution, however it's a little long-winded and requires a Mac:
- Connect the iOS device to a Mac and create a backup using iTunes
- Open the backup using an explorer/editor tool such as iBackupBot (I was a little dubious about using this at first, but it was signed by a registered developer and did not require installation nor did it ask for a password input at any stage, so pretty safe)
- Navigate to the folder "User App Files > com.apple.mobilesafari > Library > Webkit > Website Data"
- Delete all files and folders in the enclosed IndexedDB folder - this is where the 508KB of eBay data seemed to be
- Delete all files and folders in the enclosed WebSQL folder - where all the other "0 Bytes" cookies are stored. I was amazed there were even cookies in here which didn't show up in the Website Data view in Settings. Mine had a whole trove of cookies from argos.co.uk, ebay.co.uk, and uk.farnell.com amongst others.
- Restore the backup to your iOS device using iTunes
This was sucessful for me on both my iPad Pro and iPhone SE - both on iOS 10.3.3. I can't confirm if it will work for iOS 11 devices, but from what I've read many people have found the cookie problem to be fixed in 11.1.2.