Q:

Be on someone's case

From the Coach Carter movie:

I have a sister, her name's Diane. She was always on my case about
  every little thing. Matter of fact, she still is. "Turn down that
  radio. You eat the last piece of cake?..."

So what does it mean here?

A:

According to Cambridge Dictionary of American Idioms, on somebody's case is an idiom and means:

telling someone what to do or criticizing what they do

So, the meaning is:

She always criticized me about every little thing.

