There is a use of "stick" with plants that means to support the stem with a "stick". This may have led to "stickup" in a robbery in the sense of raising one's arms in the air. This may also be the sense of something sticking out.
By association, when one supoorts a plant with a stick, it stands tall. It is possible that this "stick up" for someone came to mean the same as "stand up" for someone.