Why did my Time Machine backup drive need 712GB for initial backup

Question

I recently replaced the failing 1TB drive in my wife's old mid-2010 27" iMac with a 2TB drive (OS X 10.9.4, 3.6 GHz, 8GB 1333 MHz DDR3). After bringing all of her data on board, I erased and reformatted the backup 2TB hard drive and initiated a fresh backup using Time Machine. I was surprised to see that Time Machine needed 650+GB for the initial backup. I checked the new HD and sure enough, it reported 652GB of data.
What puzzles me is that the hard drive has only four visible folders, Applications, Library, System Info and Users Info, holding 15GB, 9GB, 6GB and 30GB respectively -- a total of roughly 60GB.
Any idea what the additional 590GB of required storage is holding and whether it's necessary? Could there be old data hidden somewhere on the iMac's new hard drive? I've looked at hidden folders and files in the top level folder. There are a couple dozen or so, including one named .DocumentRevisions-V100 (from old Mac).
However, I can't display the contents of the hidden folders and they won't calculate or display the folder sizes, so all that leaves me a bit in the dark.
Any suggestions on how to identify and reduce the amount of data I'm backing up? I'm afraid the 2GB drive will soon be overwhelmed with data.
Thanks.

Answer 1

Empty the Trash if you haven't already done so. If you use iPhoto, empty its internal Trash first:
          iPhoto ▹ Empty Trash
Do the same in other applications, such as Aperture, that have an internal Trash feature.
See this support article for some simple ways to free up storage space.
You can more effectively use a tool such as OmniDiskSweeper (ODS) or GrandPerspective (GP) to explore the volume and find out what's taking up the space. You can also delete files with it, but don't do that unless you're sure that you know what you're deleting and that all data is safely backed up. That means you have multiple backups, not just one. Note that ODS only works with OS X 10.8 or later. If you're running an older OS version, use GP.
Deleting files inside an iPhoto or Aperture library will corrupt the library. Any changes to a photo library must be made from within the application that created it. The same goes for Mail files.
Proceed further only if the problem isn't solved by the above steps.
ODS or GP can't see the whole filesystem when you run it just by double-clicking; it only sees files that you have permission to read. To see everything, you have to run it as root.
Back up all data now.
If you have more than one user account, make sure you're logged in as an administrator. The administrator account is the one that was created automatically when you first set up the computer.
Install the app you downloaded in the Applications folder as usual. Quit it if it's running.
Triple-click anywhere in the corresponding line of text below on this page to select it, then copy the selected text to the Clipboard by pressing the key combination command-C:
sudo /Applications/OmniDiskSweeper.app/Contents/MacOS/OmniDiskSweeper
sudo /Applications/GrandPerspective.app/Contents/MacOS/GrandPerspective
Launch the built-in Terminal application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad. Click Utilities, then Terminal in the icon grid.
Paste into the Terminal window by pressing command-V. You'll be prompted for your login password, which won't be displayed when you type it. Type carefully and then press return. You may get a one-time warning to be careful. If you see a message that your username "is not in the sudoers file," then you're not logged in as an administrator. Ignore any other messages that appear in the Terminal window.
The application window will open, eventually showing all files in all folders, sorted by size. It may take a few minutes for the app to finish scanning.
I don't recommend that you make a habit of doing this. Don't delete anything as root. If something needs to be deleted, make sure you know what it is and how it got there, and then delete it by other, safer, means. When in doubt, leave it alone or ask for guidance.
When you're done with the app, quit it and also quit Terminal.