I'm taking a Physical Science class. How does the weight of a falling object compare with the air resistance it encounters just before it reaches terminal velocity? Just after?

You can think it through like this - when an object falls the force of gravity pulling down on it is equal to its weight:
.
Under this force the object accelerates downward (due to Newtons law ). But as it falls faster and faster the air resistance increases. This resistance is a force that is in the upwatrd direction. Let's call the air resistance force ; at some point exactly equals the force of gravity, but in the opposite directon, and at that point the sum of the forces on the object is
.
Thinking again about the formula : If F = 0, then a = 0 as well. Hence the object is no longer accelerating, and its velocity will no longer increase. The velocity at this point is called "terminal velocity."

Fom this explanation, can you tell us how at teminal velocity the magnitude of the air resistance compares to the object's weight?