The problem here is the assumption that fat is the same as heavy.

It also depends on the efficiency of the cycle.

In a theoretically friction free cycle, all objects, whatever their weight, will fall at the same speed.

Where you have to overcome frictional forces (whether aerodynamic drag, or rolling resistance, or friction in the wheel hubs), then the greater weight would be better at overcoming the frictional forces.

On the other hand, greater size will increase all of the frictional effects, not least, the aerodynamic drag.

The more interesting question might be to compare a short fat cyclist to a tall skinny cyclist, both of the same weight, and the same density (the latter point is a little artificial, since actual fat will generally be lower density than muscle or bone). In that case, the tall skinny person has a higher surface area, so if sitting upright would have higher drag, but if lying prone could reduce his aerodynamic drag to a lower level than the short fat guy.

The aerodynamic issues can also be offset by putting fairing on the bicycle, in which case the major difference in frictional effects would be in slightly greater rolling resistance to carry the heavier (not necessarily equating to the fatter) cyclist. Whether the rolling resistance increases more than the increase in mass would I suspect depend on the gradient.