How does weight influence your speed when descending? I have recently bought a road bike and went on a little trip with a friend who is also a novice.

We have approximately the same height but he weighs a lot more (I weigh 67-68kg for 1m81 and he weighs around 80-85kg). 

While descending a road, he outclassed me easily. It made me wonder :

Suppose that two people have exactly the same characteristics (same bike, same height, same equipment,...) but a different weight and a corresponding different shape (one is fit and the other overweight or more muscular). If they both ride perfectly (i.e. in an optimal manner), who is going to go faster ?

If the road and tires were perfectly smooth and there was no air, physics tells us that these two people would go at the exact same speed.

Theoretically, the heavier person has a less aerodynamic shape if his/her additional weight is the result of fat and not muscle, so if the road and tires are still perfectly smooth and if there is air, the lighter person should be faster (assuming that the "aerodynamic theory" is right).

Now, add the fact that the road and tires are not perfectly smooth and that I have probably forgotten important factors, how to know which one will be faster ?

I could have asked this question in the Physics community but I bet it is something known in the bicycles one.
The heavier person will present more area to the wind, but this is mitigated by two factors: The bicycle presents a fixed area to the wind and the area presented by the heavier person is not proportional because of the 2/3 power law. If you just scale up a rider by a factor in mass, the volume increases in proportion, but the frontal area scales up as the 2/3 power of the weight ratio because the dimension along the direction of travel does not contribute.  Both of these mean a heavy rider on a bike with a constant grade will descend faster with no power input besides the hill.