Running LR 2015.8 on a Mac, OS X El Capitan. I'm a fairly light user of LR, and usually when I am done I back up the catalog upon exiting.
This time, when doing that, I got the following message: "Catalog size is more than 4 GB." There was no way to skip the backup at this point, so I started it and quickly canceled.
If I go to Lightroom/Catalog Settings, it says the size is 14.4 MB. When I tried the backup again, after getting the same message, it actually finished the backup quickly, before I tried to cancel it. The size of the backed up catalog is 3.1 MB.
So why is it telling me it's > 4 GB when I initiate a backup?
It's just a minor glitch/bug. Just tell the dialog to "don't show again" an continue. You won't see it again.
As Robert said, its a bug in calculating the catalog size to show this information. Its harmless otherwise, just select "don't show again" and continue. We would fix it soon.