I am trying to implement a sliding drawer where handler is a button/text.
The main reason behind that is to save space. What I hope to achieve is that the drawer would open content op top of the original view. But what actually happens is that the drawer uses a relative space (button+content) in my original view.
I hope picture below will explain it more carefully. So I have a speaker icon in the drawer as a handler. I would like it to take only those 20dp or so space. When I click on the speaker, then the drawer content overlays data below. When you click on the speaker again, the drawer closes. For now, if I emulate this case, the drawer opens/closes only in the region indicated by blue rectangle.

Judging by your screenshot, your sliding drawer is inside of a LinearLayout.
Therefore it cannot do what you are looking for. (As the items in the LinearLayout will be listed linearly – therefore won’t overlay)
The documentation here: http://developer.android.com/reference/android/widget/SlidingDrawer.html says you should only use the Sliding drawer in a Relative or Framelayout (as these allow overlaying):
I would recommend the following structure: