Time Machine behaves strange

Question

While beeing away from my home studio, I´m working with three external HDs: One containig all the sample content (1 TB Firewire), one for the Logic projects including movies (2 TB, Firewire) and I recently connected an empty 3T USB2 HD as Time Machine. All HDs are formatted as Mac OS Extended (Journaled).
The three Volumes to be backuped by Time Machine (MacHD plus the two external FW-HDs for projects and samples) contain alltogether 2.14 TB. All connections are via a thunderbolt display.
When I started Time Machine off course it took a few days (running only while I was working) to fill up it´s HD. Now it claims that the HD is full, and it promises to delete "old backups" the next time it will run. That never happens though. Instead it keeps backuping endlessly and the estimated size of the backups rises constantly while the backup runs. That way there hasn´t been done a single valid backup within two weeks ...
I know that there are discussions in this forum about likely problems, but the solutions offered are too much depending on individual surroundings or I simply don´t understand them
Can anybody help??

Answer 1

These instructions must be carried out as an administrator. If you have only one user account, you are the administrator.
Launch the Console 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 Console in the icon grid.
The title of the Console window should be All Messages. If it isn't, select
SYSTEM LOG QUERIES ▹ All Messages
from the log list on the left. If you don't see that list, select
View ▹ Show Log List
from the menu bar at the top of the screen.
In the top right corner of the Console window, there's a search box labeled Filter. Initially the words "String Matching" are shown in that box. Enter the word "Starting" (without the quotes.) You should now see log messages with the words "Starting * backup," where * represents any of the words "automatic," "manual," or "standard."
Each message in the log begins with the date and time when it was entered. Note the timestamp of the last "Starting" message that corresponds to the beginning of an an abnormal backup. Now
CLEAR THE WORD "Starting" FROM THE TEXT FIELD
so that all messages are showing, and scroll back in the log to the time you noted. Select the messages timestamped from then until the end of the backup, or the end of the log if that's not clear. Copy them to the Clipboard by pressing the key combination command-C. Paste into a reply to this message by pressingcommand-V.
☞ If all you see are messages that contain the word "Starting," you didn't clear the text field.
If there are runs of repeated messages, post only one example of each. Don't post many repetitions of the same message.
☞ The log contains a vast amount of information, almost all of which is irrelevant to solving any particular problem. When posting a log extract, be selective. Don't post more than is requested.
Please don't indiscriminately dump thousands of lines from the log into this discussion.
Please don't post screenshots of log messages—post the text.
☞ Some private information, such as your name, may appear in the log. Anonymize before posting.