A bowling ball has more weight than a racquet ball.

Agreed.

Which should have some effect according to your idea of displacement.

True, it does (both calculably and in reality demonstrably).

But, If you go to your roof and released both from the same height at the same time, they would hit the ground at exactly the same time.

I am saying that they don't, but that the difference between when one hits the ground and the other one is very small. If you increased the distance, or increased your measurement precision, you would see the difference.

The "all things fall at the same rate" is a rule of thumb which is perfectly adequate for most cases we experience, but is not strictly speaking true. It would arguably be true if "perfect vacuum" were attainable - but even then not in the standard worldview (that you likely have) because there would still be the varying gravitational attraction of varying masses to consider/factor in.

We have a math formula for determining the speed at which objects will fall and the "weight" of the object is not represented anywhere in the math formula.

That's not quite right, but yes - the oversimplification taught to many students is just an acceleration and time. That is assuming there is no buoyant force, drag, etc. to consider - which is of course, untrue.

The fact that the math can still accurately tell you how fast something will fall without this concept being represented anywhere in the formula ought to tell you that you've misidentified the source of this force.

That is a mistake in your logic. It just means the variance in weight is not a major factor in the speed of the falling (assuming an over simplified "perfect vacuum" etc). Besides, what we are discussing is the the relationship of the weight to the weight of the media it displaces, which unquestionably is the cause of falling. That is in archemides' principle - so it is in "the equation".

A bowling ball has more weight than a racquet ball.

Agreed.

Which should have some effect according to your idea of displacement.

True, it does (both calculably and in reality demonstrably).

But, If you go to your roof and released both from the same height at the same time, they would hit the ground at exactly the same time.

I am saying that they don't, but that the difference between when one hits the ground and the other one is very small. If you increased the distance, or increased your measurement precision, you would see the difference.

The "all things fall at the same rate" is a rule of thumb which is perfectly adequate for most cases we experience, but is not strictly speaking true. It would arguably be true if "perfect vacuum" were attainable - but even then not in the standard worldview (that you likely have) because there would still be the varying gravitational attraction of varying masses to consider/factor in.

We have a math formula for determining the speed at which objects will fall and the "weight" of the object is not represented anywhere in the math formula.

That's not quite right, but yes - the oversimplification taught to many students is just an acceleration and time. That is assuming there is no buoyant force, drag, etc. to consider - which is of course, untrue.

The fact that the math can still accurately tell you how fast something will fall without this concept being represented anywhere in the formula ought to tell you that you've misidentified the source of this force.

That is a mistake in your logic. It just means the variance in weight is not a major factor in the speed of the falling (assuming a over simplified "perfect vacuum" etc). Besides, what we are discussing is the the relationship of the weight to the weight of the media it displaces, which unquestionably is the cause of falling. That is in archemides' principle - so it is in "the equation".