If you don’t do this, there is a good chance that some important outstanding task gets lost in the older and dusty parts of your system. When that happens, your mind is going to realise that it can’t trust the system, and it will take back the responsibility for remembering all outstanding work.
Without the weekly revision, you also don’t know whether the next actions you work on are the most important work you could be doing. Maybe the note that you created a few weeks ago is now more important.
Original source: Three principles distilled from Getting Things Done