As a lighter rider, the wind can actually hurt you a little on a flat, and a lot on a descent.

F=ma.

The heavier rider has more forward inertia than you do...and on a flat to a slightly declined road, equal wind will slow you to a greater degree.

This is offset often by the fact that you can accelerate to "cruising" speed with less energy, but assuming the wind is gusting, and not constant, each individual gust will affect you more before it dies off. The heavier rider will have greater inertia to carry him through the momentary force opposing him.

Again though...at equal power output you will be a superior climber. At less gross power output you will probably still be the superior climber provided your PWR is greater than theirs.