Final answer:
Galileo Galilei's experiments revealed that gravity acts equally on all objects regardless of their weight, leading to the insight that acceleration due to gravity is a constant. This was later encapsulated in Newton's law of gravitation, which speaks of a universal gravitational force.
Step-by-step explanation:
Galileo Galilei's conclusions about how weight affects gravity can be summarized by understanding that gravity remains constant regardless of the weight of the object. Throughout his experiments, he discovered that all objects, if air resistance is not considered, experience the same acceleration due to gravity. In his famous demonstration, purportedly from the Leaning Tower of Pisa, he showed that two balls of different masses, when dropped, will accelerate at the same rate towards the Earth's surface. This principle was further developed by Newton's law of gravitation, which presented the idea of a universal force of attraction between masses that is independent of their weight.
In response to the GRASP CHECK, Galileo's experiments support the fact that heavy objects do not fall faster than light objects because in the conservation of mechanical energy, the mass term gets cancelled, making velocity independent of the mass. The variance in velocities due to air resistance is a separate factor that does not affect the constant acceleration due to gravity in a vacuum.