Have I read the Troubleshooting Wizard before posting? Yes
Have I read the documentation before posting? Yes Yes Yes
Joomla! version: 1.5.23
PHP version: 5.3.6
MySQL version: 5.1.56
Host: ROCHEN RESELLER (shared)
Akeeba Backup Professional version: 3.3.a3
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After seeing an unexplained increase in my backup size (from 22MB to 119MB) I went into panic mode thinking I was hacked.
Before I reveal the cause, I want to point out that without Akeeba SiteDiff, Akeeba eXtract, regular backups, and a Macbook, this may have taken a lot longer to resolve.
After comparing everything I could visually inspect, it turns out the culprit is a "core" file from the webserver hosting the account. Memory contents get "core dumped" into a file when something happens in a process that the server cannot recover from.
I've since enabled a sitewide file exclusion in Akeeba Backup and all is back to normal size.
Hope this helps someone. If you haven't downloaded SiteDiff and played with it, you must try it. While it's Windows only, it's worth keeping a Windows box somewhere just for this tool!
Thanks Nicholas. Your products helped me solve this in an hour.