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You are backing up your backup archives. Please try excluding the backup output directory using Akeeba Backup's files and directories exclusion button.

If you would like me to provide more specific instructions, please ZIP and attach your backup log file to your next post. Thank you in advance!

Here's a simple trick to find large files in your backup set. Search the log file for "large file". It comes up with this result:

<root>/administrator.zip - size: 1940971418

So, basically, something on your site (not Akeeba Backup) -or yourself- has created a file named administrator.zip in your site's root with a file size of 1940971418 bytes, or 1.80Gb. My educated guess is that you have a CRON job set up on your site which is ZIPping your administrator directory and placing it into that file. Since the default backup output directory is inside the administrator directory, you have an ever expanding backup archive.

Quick example:
- The size of the administrator directory is 5Mb and you install Akeeba Backup.
- You take a 10Mb AB backup archive of your site.
- The CRON job runs and creates a 10 + 5 = 15Mb archive in the site's root.
- You take a new AB backup. Now it's 10Mb + 15Mb = 25Mb.
- The CRON job runs and creates a 25 + 10 + 5 = 35Mb ZIP file.
- You take a new AB backup. Now it's 10Mb + 40Mb = 50Mb.
- The CRON job runs and creates a 50 + 25 + 10 + 5 = 90Mb ZIP file.
and so on and so on... increasing the backup archive exponentially.

Solution:
Step 1. Remove the CRON job which creates that ZIP archive
Step 2. Exclude that ZIP archive, for good measure!
Step 3. Take a new backup and test it. It should restore properly and not have the administrator.zip file in it.
Step 4. Delete the administrator.zip archive from your site's root
Step 5. Delete your old (bloated) backups
Step 6. Never, ever, create such a CRON job unless you are perfectly sure that you want to bloat your backup archives for no good reason ;)

CRON is a system-level service to run tasks on a schedule. You can ask your host to help you with reviewing your scheduled (CRON) jobs. If you had someone perform server-level work for you, you can also ask them as they were probably the ones installing that scheduled job.

You're welcome!

I removed the log file. I'd like to keep the (otherwise anonymous) thread so that future searches can benefit from it.

Done!