The substitute spring you fitted is the governor spring, and it has to be exactly the right length and tension to work. The function of the governor spring is to try to open the throttle, and the mechanical part of the governor tries to close it. The speed control sets the amount of spring tension that the mechanical part has to overcome to keep the engine from running faster than you want. Since the mechanical part is winning the struggle, your substitute spring seems to be applying insufficient tension, because it is either too long or too light. The only practical cure is to obtain the correct spring. It is lucky the spring was too light: if it was too heavy you'd probably have a broken connecting rod right now.
To answer your specific question, the engine will not speed up when it is put under load. The governor's function is to keep the speed constant regardless of load.
