There seems to be some misinformation here. I can't entirely correct it because I don't have all the information.
First and foremost, how big is your startup drive? How big is your time machine drive? How much space is free on each?
Without knowing those exact values, it is hard to say anything for sure.
I can definitely tell you that if you are noticing any problem with Time Machine, then Time Machine is not the problem. The last thing you want to do is turn it off. Find out what the problem is first. Time Machine runs in the background. If your machine is healthy and you are using a locally connected external drive, you should never notice Time Machine is running.
How old is your computer? How old is the internal hard drive in it? Your internal drive may be beginning to fail.
For the record, that error code is entirely meaningless. There are many such messages printed in system logs. They aren't meant for end users to dechipher.
Local backups are simply Time Machine running without using the external hard drive. If you have a notebook machine, Time Machine always runs, even if your backup drive is not connected. It is not correct to say that the local snapshots only contain a week's worth of files. They contain all changes but are coalesced daily and weekly, just like regular Time Machine backups. When you connect your external drive, they are all moved to the main Time Machine disk. If you are noticing that the local backups are running, then something is seriously wrong. One possibility is that you are using Parallels/VMWare/VirtualBox or Entourage that is not optimized for how Time Machine runs. Parallels and similar programs have settings to allow you to exclude their data form Time Machine so you can back it up manually. If you aren't using these problems, and you are noticing local backups, then your internal hard drive is either full or about to fail. If the drive is close to 3 years old, either could easily be true.