Why is Time Machine telling me my disk is too small while Disk Utility tells me I have 3X the empty space I need?

A month or two ago I installed a new TM disk that is roughly three times the size of the selected files and folders to be backed up, and, in fact, larger than the whole boot disk by about 150%. I was careful to wipe the new Time machine disk before assigning it to TM, and careful to "exclude" almost everything from backup but my User folders. Even Applications is excluded. Now I'm getting notifications from the OS that there's not enough room on the disk to back up anything. Supposedly it needs another 4TB to back up a 3TB boot drive, less than half of which is supposed to be copied. And at the same time, when I scrutinize the Time Machine disk in Disk Utility, I am told the 4TB TM disk only has 1.35TB in use, and 2.65 TB free space. Somebody got some 'splanin' to do. If necessary, I can just reformat the disk and start over, since I have a functioning clone backup as well, but I'd rather find out what the problem is. I've been told that I should have a TM disk that's significantly larger than the drive to be backed up-OK, the ratio is 1.35 : 4.0; assuming that the TM disk starts overwriting when full, why am I getting this doodah at all?