Q: Trouble with Time Machine

When you first connected the external drive to your computer it backed up the entire computer. After that TimeMachine makes a backup of only the things that have changed since the last backup. And so it goes day after day month after month. TimeMachine erases nothing until it doesn’t have enough space to make a backup. Then it gives a warning before deleting the oldest partial backups - enough to make room for the newest backup it needs to make. This ensures that TM has copied everything that your computer has on it now along with some more recent backups in case you messed up a file, didn’t realize it, and the messed up file was backed up.

If you click on the TimeMachine icon in the menubar the dropdown menu will tell you when the last backup was made. It should be very recent and if it is you’ll know TimeMachine is working exactly as you want it to. If you’d rather not get warned each time TM deletes more old partial backups open TimeMachine preferences and click on the options button. There’s an option to select that will stop telling you that TM is running out of room. Now the most recent TM backup is some days ago that means TM really isn’t doing any backups which indicates a problem. If that is the case let us know.

This website has lots of information about TimeMachine. This page specifically deals with backup errors due to the disk being full and this page tells how to delete files using TimeMachine.

An 119 GB backup is very large especially if the last backup was within a day or two. Even if you were in the Sierra public beta program the backup would have been less than 20GB. I suspect there’s more to this story. Has anything out of the ordinary happened since that last backup was done? Do you have other external hard drives connected to the computer? TimeMachine can backup up external drives that are connected to the computer. You might open TM preferences and see what’s being excluded, if anything.

Do you use this external drive for things other than TimeMachine? It isn’t a good idea to do so.

When you enter Time Machine, you see windows cascading back in time. The frontmost window represents the current state of the data, and the ones behind it represent successive snapshots of the data taken by Time Machine. Is there only one snapshot (that is, the one behind the front window), or more than one?

That may mean that you've backed up more than one volume (what Apple calls a "disk") or machine to the same destination. It could be the result of erasing the primary volume, depending on how you restored it.

Time Machine will delete older snapshots when necessary to make room for new ones, but it will never delete the last snapshot of any volume or machine. So you can end up without enough space for a new snapshot.

You can try to delete old backup folders by dragging them to the Trash, but often the Trash will then fail to empty completely with strange error messages, and you then can't empty it at all without erasing the volume, nor can you put the folders back where they were.

The best course of action is to stop using the backup drive until you're sure you'll no longer need the data it contains. Then erase it and start over. Meanwhile, start another backup on a different drive. You should do that anyway, as one backup is not enough to be safe. If you're backing up to a Time Capsule, you can connect a USB hard drive to it and back up to that.

Please read here > Repair disk permissions with Disk Utility - Apple Support