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Upgrading Joomla has absolutely nothing to do with this. We are of course upgrading all of our sites within 6 hours of a new Joomla version being released. Not just our live sites but also our development and testing sites. I can assure you that none of our sites and none of our client sites exhibited this kind of behavior, nor could they possibly do that. After all, Akeeba Backup backs up what is on your server. The Joomla version installed is largely irrelevant – it only adds up a few dozen kilobytes on each new release, if that.

Most likely you are backing up old backups or large files.

One reason is that you followed the instructions in Akeeba Backup's message about creating a new backup output directory outside the site's root at the same time you update Joomla. I think that you missed, however, the part where it told you that you should be excluding the previous backup output directory (default: administrator/components/com_akeeba/backup) from every backup profile.

If this is not the case, you have some large leftover files which were created outside Akeeba Backup. For example, you might have zipped up your entire site. Unless you explicitly tell Akeeba Backup to exclude these files it will include them in the backup archive.

Something doesn't add up and your screenshots don't help clarify the situation, I'm afraid.

In your screenshots I do not see the default backup output directory, administrator/components/com_akeeba/backup. Does it exist? If it exists, have you excluded it from both backup profiles?

What is the backup output directory for each of the backup profiles? If they are different, are you excluding the other profile's backup output directory from each profile?

Also note that you don't need to exclude the current backup profile's output directory. It is automatically excluded.