To measure the "effect" of weight on bike performance, you need to appreciate some of the laws of physics. Namely, that a object (w/mass) in motion wants to stay in motion. That answers the question, "Why isn't it easier to "ride" (maintain a constant speed) a light bike than a heavier bike?"

Unfortunately for us earthlings, the laws of physics also say that in order to accelerate a bike (acceleration in physics is a bit different than its usual use because it means both changing speed up AND down) you need to take into account its mass (weight). Heavier bikes take more energy to accelerate than lighter bikes.

It is the second point, that acceleration qualities are different, that make a light bike such a pleasure to ride. You can ride faster, in the sense of making better overall time, on the light bike with less effort (energy).