why do two objects fall same rate in a vacuum

[MigL]

Yeah, I read about that example one time.
Except it was, what happens if you put a bowling ball and a ball bearing in a paper bag and drop the bag from height.

[Chopsticks]

Folks upthread covered the theory and thought experiments, now here's the line of reasoning leading to a practical experiment of the theory (used in at least one science museum, and IIRC was Galileo's real experiment)

1. Objects fall at the same speed. Okay, so they should still fall at the same speed if they fall next to a vertical surface, since they aren't touching it.
2. Let's make the vertical surface really smooth (a good sheet of ice say), then tilt it just a little from vertical, and drop the objects from the top. The objects still fall down, but the surface deflects them sideways. Since it is a frictionless surface it won't change the speed, just direction
        2a Changing the direction means you change the velocity from totally vertical to a mix of horizontal and vertical. This means things fall more slowly, so you can see the experiment without a high speed camera.
3. Make the angle flatter and flatter, you get the experiment of two weights sliding down a low hill
4. In the real world, you want to make your objects as similar as possible so they are equally affected by friction, and by air resistance.

Experimental setup.  A nice smooth plank, one end on the ground and the other liftable to various heights. Two same-size empty boxes that are smooth on the bottom (some of those smooth plastic furniture sliders on the bottom maybe).  Put one pound of anything in one box, two pounds of anything in the other. Slide them both down the slope. Alternatives could be spheres or cylinders - important thing is same size and outer material (bowling ball and an identical bowling bowl hollowed out on the inside, car tire with and without some weight evenly distributed around the inside so maybe a tire with and without a hub)

Adam Savage & Vsauce built a really nice example of this kind of experiment setup. Theirs demonstrated different types of hill, but could be used for this experiment if you added weight inside one of the rolling things, maybe hollowed out #2 and kept #3 unchanged. Then start all 3 objects at the same height. Youtube link: Adam savage's slide

[mistermack]

My own picture of this is pretty simple. So it may be wrong, but here goes. 

If you have two identical steel balls, and hold them a metre apart, and drop them from an upstairs window, you would expect them to land simultaneously. They are identical in weight and size, so of course they would. 

Do the same thing with them a half metre apart, and the same thing happens. Then 10 cm apart. Then 1 cm apart. They both still fall at the same speed. Even 1 mm apart, they both fall at the same speed. So why would you expect anything different if they were 0 mm apart? ie touching. Neither is going to fall faster or slower than the other, and hence affect the speed. If you glued them together, that's not going to change. So you've established that an object twice the size and weight of a single ball will fall at the same speed as a single ball.