Thanks Parcel32. 
So where are we at here? Haven't been backing up for two weeks now.
Hi Parce32.
Sorry to have kept you waiting but I myself have been waiting for guidance as how to best extract data from your system to understand this problem, but none has arrived yet, so I suggest we go ahead with tidying up and moving on.
What I am going to propose is that you delete the N360_BACKUP folder (which I believe is now around 303 GB). Then get you to run the backup again to the disk you just deleted the N360_BACKUP folder from, and then consider creating a second backup set to provide further security in future. If you are content with this - read on. If not say so and I will do my best to respond.
Without making any changes to N360, open up Microsoft Explorer and look at the 1 TB drive. Select the N360_BACKUP folder and select delete. If asked to confirm or warned that it is too big to go in the recycle bin, do not worry - proceed. However - note that given the size of the file it is likely to take some time to complete. Leave the system running until it reports a successful deletion. Go back to the disc again and check that the folder has gone.
Next open N360 and select the backup pane; select Manage Backup sets, check that the correct set is selected and that on the "Where" pane the 1 TB drive is the target. When you can afford to leave the machine quiet for a while, but with power set so that it does not go to sleep, hit the "Run Backup" button. Wait for this to complete and check that it reports a successful backup. If not come back and let us know what it says. Assuming that it is successful look again at the 1 TB drive and confirm that there is once again a N360_BACKUP directory and note its size. It should be around 44 GB from what you said before. If this is the case then you have a good backup of the appropriate size back on the disc you want it on, and a lot of free space. 
All should now be well and you can choose to run this backup manually or by one of the other options given on the "When" tab. Some people like the Automatic as they do not have to worry about it, myself I prefer the manual as I know what is happening and when. The choice is yours. The next backup should just add any new or changed files to the backup folder and the size of the backup folder should change only slightly.
However..... as you are aware, sometimes the size of the backup folder can grow substantially and this can cause problems. I have found that the problem can invariably be resolved by just deleting the folder and starting again (as above). However this can leave you exposed without any backup for a short period. So the solution I adopt is to create a second backup set, identical in all ways to the first apart from its name. I run this at a slightly different time from the first and this gives me two backup folders within the N360_BACKUP folder. Now if either of these backup sets starts to get too large I can delete it knowing that I am still protected by the second set. A bit belt and braces but it is simple and seems to work for me. If you had sufficient space on another external drive then you could even consider running the second backup set to a different drive which would make you even safer, but most people will not want to bother with that.
I hope the above makes sense and helps you. Do come back with any questions and please do keep us informed of how you do.
Good luck.