How do I continue to use Time Machine backups after switching my hard disk? I replaced my HD with an SSD (256 GB), and restored the contents from my Time Machine backup (external HD 320 GB).

Now, after a day of working, I plugged in my external HD to make the next backup. Time Machine now started to scan my files, prepared the files etc. (took rather long, because it somehow needed to scan everything), then entered the "Deleting old backups" phase. Everything looked normal, but just when it was about to finish, it failed with "This backup is too large for the backup disk.".

Only about 200 GB of my SSD are used, so this should easily fit on the external 320 GB HD: Not many files have changed since the time I restored the backup.

When I look into the Time Machine drive, I see, that it has automatically deleted all my old versions already I'm really not happy about that! Only the latest one is left - the one I restored from yesterday, and now it seems to create a separate backup for my new disk? Ok, "200 GB x 2 > 320 GB", but that's not what it should do. It should just continue writing the differences, as it has always managed to keep several old versions, so why would it be any different just because I moved the contents to an SSD? 

Is there a way to make Time Machine "reconnect" to the new SSD (I assume, it is still somehow "connected" to the old HD, and therefore doesn't treat the changes on my new SSD as changes to the backup?)

I wonder, if I should have rather cloned my HD (e.g. with a third party tool), without Time Machine knowing about it?
From http://simon.heimlicher.com/articles/2012/07/10/time-machine-inherit-backup-using-tmutil


  Time Machine uses a unique ID (UUID), which is specific to a volume
  (i.e. a partition of a disk), to associate the volume with its backup.
  In OS X releases before 10.7 Lion, when people exchanged their disk or
  migrated to a different Mac, this feature has made it difficult to get
  Time Machine to continue adding to the backup history of the
  previously used disk.
  
  In OS X Lion and now also OS X 10.8 Mountain Lion, there is a nifty
  new Terminal command called tmutil, which makes this whole drama a
  breeze.


Here's the command

sudo tmutil associatedisk -a "/Volumes/Macintosh HD" "/Volumes/Time Machine Disk/Backups.backupdb/John Doe's MacBook/Latest/Macintosh HD"


See also How can I use an existing Time Machine backup with my new computer?