Great question! I think the best way to tackle this is by thinking about forces and acceleration.

An object traveling through the air experiences a force that will eventually control its distance. We can separate the force on that object into two parts.

The first force is gravity. This force is directly proportional to mass: the more mass the object has, the stronger the force of gravity will be. Because of this, it turns out that gravity does not matter when we compare distance traveled by objects with different masses.

The important part of the force is air resistance, also called drag. The drag force is proportional to the speed of the object, because the faster the object is moving, the more air molecules it will bump into, slowing it down. But this force is not affected by the mass of the object.

Now we want to know how the speed of the object will be affected by the force. In physics, instead of saying "the change to the speed," we usually say acceleration--it's the same idea. (Just keep in mind that in our problem the acceleration is negative--it's "deceleration.") To find the object's acceleration, we take the force and divide by the object's mass. This is known as Newton's second law of motion, which we usually write as F = ma (the force is mass times acceleration).

So let's say we have two objects with the same size but slightly different masses, and we throw them at the same speed. Both objects will feel a similar drag force, but the effects on their speed will be different, according to a = F/m. The heavy object will feel small changes to its speed (its acceleration is close to zero), while the light object will slow down a lot (its acceleration is a large negative number). In the end, the heavy object will travel farther, since it was less affected by air resistance.

Now that you've seen this example using Newton's second law of motion, we can use a "shortcut" for this kind of problem by thinking about inertia. Inertia tells you how much an object resists changes to its speed. The more inertia it has, the more force it needs to speed up or slow down. Newton's second law of motion tells us that inertia is just mass. (Well, at least in this case. There are different types of inertia for dealing with changes to other types of motion like rotation.)

If you try to test this in an experiment, there is one more important thing to consider. If you throw two objects "as hard as possible," it's possible that you are applying the same force to both objects--and as we talked about, that's different from causing the same acceleration. If you apply the same force to two objects, the heavier object will end up being launched at a lower speed because of its high inertia. To fix this, you want to accelerate both objects for long enough to get them to the same speed.