Hi. Physicist here. You are absolutely wrong. The mass of an object does not affect the magnitude of force of air resistance which acts upon a falling object. But the acceleration that object will have is given by Newton's second law as Force divided by mass. So a heavy and a light ball with the same shape will experience the same air resistance, but the heavy ball will "care less" and thus fall faster.

But it does affect the downward force acting on the object. Given two objects of the same shape but with different masses, one will indeed fall slower than the other. This is because the ratio of weight to surface area differs a lot between the two. Here's a calculator from NASA you can play with, and a relevant passage from the same page:

If we have two objects with the same area and drag coefficient, like two identically sized spheres, the lighter object falls slower. This seems to contradict the findings of Galileo that all free-falling objects fall at the same rate with equal air resistance. But Galileo’s principle only applies in a vacuum, where there is NO air resistance and drag is equal to zero.

https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/termvel/

A ping-pong ball sized lead shot and a ping-pong ball both fall at the same rate though air?

That doesn't sound right.