I don't know about the file size discrepancy, but you might consider setting up a drop box account. That's how I copy files back and forth and it's much easier than using iTunes. Plus, it leaves a copy of the file "in the cloud" so a copy of your file is safe even if both devices were lost or destroyed.
On the iOS device, I open the drop box app, find the database file and try to open it. When I get an error message that it can't be opened, I use the "open with" option to open it in FileMaker GO. This copies the file into the Fm GO "sand box" and if there is a copy in place already, I'm asked if I want to replace it.
To send files the other way, I select the "files on device" option, tap the control at the top of the screen that has a check mark in it. tap to select the file and then tap the "send" icon (up arrow from a box) to send the file back to drop box. I can then open drop box on my lap top and pull a copy out of the drop box folder.
Is it just me, or does the transfer back to Dropbox hang forever...? I'm working with a fairly small file (1.5 Mb), but the iPad has been stuck on "Uploading" for nearly five minutes.
UPDATE: My bad. Realized the hang was caused by pages still being open on the iPad. Once I circled back, closed the pages, then tried again, transfer back to Dropbox whizzed along.