Remember Kim, that on earth the is not often 'one' simple action and reaction force.
If you are do a standing curl of a dumbbell, the dumbbell will give a force back. But you are also fighting the force of gravity in that situation. So now your body has to act against two forces. You compensate by expending more energy.
As dave said, there are no equal and opposite forces. If the horse and wagon were in space, (bear with me :) ) once the horse got the wagon up to the desired speed, the horse would not have to expel any more energy to move it. In space, once that wagon is moving, it will keep moving until something acts upon it, like the wagon hitting an asteroid. On earth, gravity, friction resistance, and air resistance are all forces that act on the wagon when the horse pulls it. To keep the wagon going, the horse has to continually expend energy. The amount of energy a horse expends depends on all the forces the horse must overcome to pull that wagon.
You expend energy to combat the forces acting on the dumbell. If you exhert more energy than the other forces acting on it, you will move the dumbell.
Think of weight as simply a measure of gravity acting on something. You might find it easy to curl a dumbell that weighs 10 pounds. You will have a harder time curling a thousand pound barbell. Why?
In the famous E=Mc2 equation, the energy of an object is the mass of the object, multiplied by speed of light squared. The heavier an object, the more potential energy it has, and therefore, the more energy you as a person need to expel to move that heavier object.