Does a heavier person go downhill on a bicycle faster than a lighter person?

In the absence of Aerodynamic Drag, the answer would be no, they will accelerate at the same rate down the incline. However, considering we do have this air stuff all around us that we require to breathe, the heavier person will accelerate faster down the hill and therefore end up taking less time to get to the base of the hill.

Looking at a hypothetical free body diagram, there would be the force of drag up the hill, the force normal up and perpendicular to the incline and the force of gravity straight down. It would be logical to break the force of gravity into its components, one parallel to and down the incline and one perpendicular to and down the incline. The acceleration of the individual would be found by using Newton's second law in the direction parallel to the incline.

The two forces parallel to the incline are the force of gravity parallel and the drag force. The force of gravity parallel will increase the magnitude of the acceleration down the incline and the force of drag will decrease the acceleration down the incline. Because the force of drag is independent of mass, it will be roughly the same for both individuals. However, the force of gravity parallel to the incline will be increased for the more massive individual and therefore so will the acceleration.

If you want to know more about the Force of Drag, I have an entire video which goes through the specifics and even uses a spreadsheet to do some calculations.

You can find the lecture notes here:
https://tutor.hix.ai

And I also did a problem in class that involves a lot of what we talked about here: