Originally Posted by FBinNY

Bicycle riding consists of riding against two major sources of resistance, wind drag and gravity. There's also tire, chain and bearing drag, but those are very minor in the scheme of things.

On level ground, weight is only a factor when accelerating, so the bulk of your work is against wind drag, which is proportional to the square of your speed.

However on hills, you're working against gravity and the bulk of your effort is simply lifting yourself to higher altitude (why climbing stairs is so much harder than walking on level ground). But most people don't ride as fast when climbing, so wind drag is diminished and becomes less of a factor, and on steeper hills almost negligible. That leaves only gravity which (obviously) is proportional to your weight.

So you get a curve, where being lighter produces only a minor improvement on level ground, and a major improvement climbing.

BTW- with improvements in aero the curve is pretty much reversed, with the most benefit at the higher speeds on level ground (or downhill), and greatly diminished at the lower climbing speeds.