If all you're going to do is fly level laps with maybe climbs and dives, then even a 7-8 pound airplane with a 40 may work OK on control line. That's assuming that it doesn't pull you off your feet.
But most of the guys here are thinking "stunt", and control line stunt is far more akin to RC 3D in it's airframe and power plant requirements than it is to RC warbirds.
Basically with stunt you're routinely carving figures in the sky whose diameter is about 12 times the airplane wingspan, some of those maneuvers are required to have corners that are more like 2-4 times the airplane wingspan, and some of those maneuvers are required to be done straight overhead, with the airplane basically being held up by centrifugal force that's maintained by the engine pulling the plane straight up.
And for stunt you're locked into whatever the engine does by itself -- consequently, engines are adjusted for steady runs or possibly for runs that give you more power when you need it. This means that the peak power available is considerably less than the power available from the same engine when it is set up for RC.