Can't copy Time Machine backup to new drive

Hey there,

my old backup drive is ~1 TB and the new one 2 TB. So I tried to copy the Backups.backupdb exactly as described here: Time Machine: How to transfer backups from a current backup drive to a new backup drive - Apple Support

However, the copying process does not stop at 1 TB (size of the Time Machine backup) but continues until it exceeds even the 2 TB and is then cancelled because the drive is full (obviously).

After cancelling the process only three or four backups were copied to the new drive, although there are much more on the old drive.

Has anybody else experienced this problem and found a solution?