Why did we specify the use of a “light” spring for the experiments described in Section 3-3? What would be the difference if we used a “heavy” spring?

Springs come in different stiffness, requiring different efforts to stretch them. The effort needed to stretch a given spring increases as we stretch a given spring increases as we stretch it through larger distances.
In the light spring the uniform of the elasticity will be maintained throughout the spring since the spring is light and it will not stretch due to its own light mass. Therefore any other forces will not effect on the motion of the body which is attached to the spring. That is why we specified the use of a “light” spring for the experiments described in Section 3-3.
In a heavy spring, the spring will stretched due to its own mass. So the uniform of the elasticity will be damaged and it will stretch due to its own heavy mass. Therefore other forces will effect on the motion of the body which is attached to the heavy spring.