Weight does not directly affect the falling speed of objects in a vacuum. In the absence of air resistance or other factors, all objects, regardless of their weight, fall at the same rate. This principle is known as the "equivalence principle" and was famously demonstrated by Galileo.
However, when objects fall through a medium like air, the presence of air resistance comes into play. Air resistance opposes the motion of the object and can affect the rate at which it falls. In this case, weight does become a factor.
Heavier objects have a greater gravitational force acting on them, which means they experience a larger downward force. This greater force results in a higher acceleration and faster falling speed. On the other hand, lighter objects experience a smaller gravitational force and thus have a slower falling speed.
When considering objects like rocks and feathers, the difference in their weights leads to different effects due to air resistance. Feathers have a large surface area relative to their weight, which increases the air resistance acting on them. This increased air resistance slows down the feathers' fall, making them descend more slowly compared to heavier objects like rocks.
In contrast, rocks have a smaller surface area relative to their weight, resulting in less air resistance. With less air resistance, rocks are less affected by it and can fall more quickly through the air.
It's worth noting that the effects of air resistance become more pronounced at lower speeds. In a vacuum or when objects reach terminal velocity (the point where the force of gravity is balanced by the force of air resistance), weight no longer plays a significant role, and objects fall at the same constant speed regardless of their weight.