Can't Backup to Time machine

I had to have the old hard drive replaced on my macbook pro running Snow Leopard 10.6.8 operating system.   It was replaced at the apple store.  I brought it home and yesterday restored it from the last time machine backup of my old hard drive which was Friday.  That appears to be the only backup on the external hard drive I've been using with Time machine.   Today, it gets an error message.
Time Machine could not complete the backup.   This backup is too large for the backup disk...etc.  
It is almost like it is trying to completely back up the new hard drive even though it was just restored from it.  Is it because it thinks it is a different drive or something because it is a new hard drive?
What do I do?  I don't want to delete the one good backup that I have but, I want to be able to use time machine to back anything up.
BTW, have called Apple Support who may be looking into the issue....haven't heard back yet.
Thanks in advance.


I'm somewhat sure that TM sees the new HD as an entirely different computer, so there's not enough room foro the old backup and the new one. If you erase the external HD, TM will probably work just fine.
I would not recommend using TM as your only backup. It takes every file on your had and makes one big giant file out of it. One thing goes wrong with the backup file, and your backup is gone.
Consider another external HD that you use something like SuperDuper or CarbobCopyCloner to manually make another backup every so often in addition to the TM backup that happens automagically. You may also consider an online backup like Carbonite or CrashPlan. Those are automated and provide the added security of an off site backup.