Apple - Increase size of sparsebundle for TimeMachine

  1. Double-click the sparse bundle to mount the Time Machine Backups or Backup of <computer name> partition (but don’t select it). That may take a moment.

  2. Select the sparse bundle again, and click the Partition tab towards the top of the window.

  3. Type the desired size in the space provided, or, in the diagram that appears, drag the lower right corner of the partition all the way to the bottom to fill the volume, or drag it upwards to shrink it, click Apply and confirm.

  4. As part of the process, Disk Utility will do a verification of the data in the partition, so it may take quite a while. You can see the log of what it's doing by selecting Window > Show Log in the menubar.

  5. When done, and you quit Disk Utility, you may get an Operations still in progress message. As long as the log says "Partition Complete," it's done, so click Close.

  6. Eject the sparse bundle before starting the next backup.

Source: http://pondini.org/TM/A8.html