Time Machine not deleting old backups

Time Machine deletes older files if they have been deleted from the source when it needs space on the backup drive for a new incremental backup. Time Machine "thins" it's backups; hourly backups over 24 hours old, except the first of the day; those "daily" backups over 30 days old, except the first of the week. The weeklies are kept as long as there's room.

How long a backup file remains depends on how long it was on your Mac before you deleted it, assuming you do at least one backup per day. If it was there for at least 24 hours, it will be kept for at least a month. If it was there for at least a week, it will be kept as long as there's room. By default, Time Machine backs up hourly. That cannot be changed in Time Machine. There are third-party utilities that will modify the backup interval such as Time Machine Editor.

The Time Capsule sparse bundle grows in size as needed, but doesn't shrink. Thus, from the user's viewpoint of the Time Capsule, it appears that no space has been freed, although there may be space in the sparse bundle.

Once Time Machine finds it cannot free up enough space for a new backup it reports the disk is full. You can either erase the backup drive and start over or get a larger drive.

You need at least 2-3 times the capacity of the source. In your case, you are near the minimum as relates to your data. If the source drive is 1TB as is the backup drive, then you don't have a large enough backup drive to meet even the minimum size needed.

Time Machine is an accumulating backup utility because it retains past backups. Even pruning the files to keep disk usage down will not prevent the backup drive from becoming fuller over time. How much time depends on how often the data on the source changes and how much data changes per day. Time Machine does hourly backups, so every change is backed up each hour. If you run a Windows emulator like Parallels using a minimum pseudo-disk of 20GBs, then even so much as a one-byte change will cause Time Machine to re-backup the entire 20GBs. This would cause the backup drive to fill up in days.

There is no escaping the problem of an accumulating backup. All backup utilities that keep changes will fill up their backup drives in time. To avoid that you can use a backup utility set to over-write changes. Then you can use a backup drive that is the same capacity as the source drive, and never run out of space. However, you can never "go back in time" to recover a backed up file you have already deleted or over-wrote.

If you continue using Time Machine but want to extend the life of the backup drive, then you can change the backup interval using a third-party utility such as the free and excellent TimeMachineScheduler. There may be another such utility out there but I have used this one when I once used Time Machine.

Let me add that when it comes to backups, you can't have too many. I maintain three separate backups in case the main backup drive fails or becomes corrupted. You can keep all your precious backups by simply removing the backup drive and replacing it. Put the old drive in a safe place should you ever need it.