Mac – Time Machine not backing up

TimeTracker is a quick-and-dirty application that displays the contents of your Time Machine backups, and shows what's changed since the previous backup.

I believe this is a staleness prevention. That whenever there is too long between backups Time Machine uses a more thorough way to ensure that the backup is complete.

It is my understanding that the 40 GB is a "this is how much we consider for backing up" and that the actual data transferred may prove to be a lot less if the files turned out to still be identical.

Based on your description I believe that you have reached a point where you need to let your Time Machine backup catch up - work on its own until it is done, if at all possible. If you cannot wait for that, perhaps now is a good time to buy a new drive and use that instead and have the old drive as a backup backup.