This is for small aircraft only:
Think about it as a flow from the control input (stick/yoke) to the control surface. You move the stick, which pulls one end of a cable that is strung through the aircraft and the other end is directly attached to the control surface. So if you move the stick 2 inches to the left, it pulls 2 inches of cable through the system, and moves the control surface 2 inches. If you pull 4 inches, it pulls 4 inches of cable and moves the control surface 4 inches. These are just random numbers I pulled, real values depend on a particular aircraft design, but you get the idea?
Get some string and try it yourself, if you pull on one end of the string, the other end moves the exact same amount. You can't pull the string 1 inch and have the other end move 1 inch, then pull the same exact string another 2 inches and have the other end move 4 more inches. To do this, you would need a complicated system of pulleys and cams and whatnot, which all adds a lot of weight to an aircraft, which is a big no-no in aircraft design.
Higher performance and larger aircraft use assisted control systems and since they usually have a little more power available, they may have mechanical systems that allow them to have a curved response.
Here's a good page that discusses this, with a cool picture of a portion of an F-15's flight control linkages: http://2.bp.blogspot.com/_WX4wJ_9qjS0/TMBbv0J9TTI/AAAAAAAAAGs/q7y_L8ejCKY/s1600/F-15_Lateral_Control-1.jpg