Help with Time Machine

Have you tried manually deleting other backups so there is space on the drive?

 

Opps! Be careful. If you manually delete other backups, you should delete only the oldest backup, or risk disrupting the TM logic.

 

Turning off TM (unchecking backup automatically) doesn't work? Or if you have multiple TM disks, just removing the disk?

 

If there is no more room for new backups and you want to keep all old backups then it is time to start using a new backup drive, of course. There doesn't seem to be a way to keep selected archived files in the TM system. As madrich points out, TM uses a complicated logic for storing files and so changing any files could make it unusable.
I would be investing in a new hard drive if the old files are that important. In any case it is recommended that you use at least two separate hard drives for TM, which automatically alternates between them if they are both mounted. You could even investigate copying the old backups (in full) to a new larger hard drive and see if TM recognises it and starts using it without erasing old files (until it is full).