>     If I move the curve, actually I click on the curve and it seems
>     to move the data points, then I can change the line
>     thickness/color
  To simplify things I would advice to select "Status Bar" option 
from the drop-down menu. This will should you what kind of the object 
the mouse is crossing. Just you realize the mouse is becoming in 
touch with very your object - click "RIGHT" mouse button to generate 
the "context menu".
                    Valery