Everything is working as expected.
I'm not a programmer so this explanation is from a layman's perspective. Two gigabytes is a magic number in PHP. That's where the integer type changes to a real type (reals have decimal places, integers don't). When we're talking about backup archives, integers are good, reals are bad. A backup archive greater than 2Gb may be corrupted simply on its size. So, by default, 2Gb is the largest file size that Akeeba Backup will create. When your backup archive reached that size, it was split into multiple parts. If you've used multi-part zip or rar archives, it works exactly the same way. Kickstart looks for the jpa part (or jps) and the j01, etc. are handled behind the scenes, invisibly.
You must have all of the parts of the archive in order to restore your site. All of the parts need to be in the root of the site along with kickstart.php. This doesn't apply to an internal restore from the Manage Backups screen, everything works behind the scenes there.
Dale L. Brackin
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!
My time zone is EST (UTC -5) (click here to see my current time in Philadelphia, PA)