Update 4/19/13.--I have found how to look at the history of the com.apple.backupd logs to see when the problems occur and saw on the 17th from 5-8 pm and the 18th from 2-5 pm the backup ate just over 50GBytes each time, reducing the free space by 105 GBytes.
That's not so much a problem down the road as the backup will erase memory for each backup when the disk is full, but it only causes the backup to take longer and start doing it earlier. As it is, this will eat a 1 TByte HD in under two weeks.
What I also know is nothing is wrong with the TC HD, nothing with the sparsebundle file and nothing with the spotlight files on the TC or the HD, so it's only left to the software which goes nuts every now and then for unknown reasons.
Original Post 4/17/13.-- It seems I likely misunderstand how the backup works. Reading what information I could find says it makes hourly backups, then a daily backup and then a weekly backup. If that's true, then it creating a lot of copies of files it doesn't really need.
This does describe part of what I see but not everything. The hourly backup takes a few minutes and the daily backup, if it's backing up the previous day, explains the excessively long one backup which takes 2-3 hours or more but still that's excessive as the overnights with another applications are relatively short (10-20 minutes).
What I'm trying to find is where the com.apple.backupd logs are kept to see where the large jumps are in the backup and available space. In the past the daily log hasn't shown a consistent time for these jumps as the occur days apart.
Anyway, more information is what is needed to understand what's happening, something Apple's Website and other Websites seems short. I'll post if I find anything new.