why kill...........spoiler

If you watch part III, it is revealed that she was not his real mother. But Norman thought so at the time. Why? Well, he killed his first, remember?

I hated that ending. It makes the entire movie pointless.

He killed his real mother so he could set her back upstairs in front of the window like old times before he was put away in a mental institution

For once, he wanted to be in control of her instead of their relationship being the other way around. Basically, by killing her, she became his "mother" in the end.

~~/o/