On a well-maintained bicycle, frictional losses in the transmission and rolling resistance of the tyres are small compared with the effect of wind resistance when riding at a reasonable speed. Frictional losses are increased by increased weight, but that is an increase in something small so we can pretty much ignore it. What really matters on the flat is how weight and wind resistance are related. Wind resistance is proportional to frontal area and weight to volume.
If you imagine a cube whose sides are 1 metre in length, then the area of one face is 1 sq.metre and its volume is 1 cubic metre. Now double the length of the sides. The area of one side is now 4 sq.metres but the volume is increased to 8 cubic metres i.e. volume increases much quicker than area with increasing size. Big cyclists don't suffer increases in wind resistance in proportion to their weight. Bigger cyclists tend to be more powerful than smaller ones, assuming that their size isn't entirely due to fat! For that reason, bigger cyclists tend to have an advantage over smaller cyclists on the flat, especially into headwinds.
In terms of climbing - on a steep hill, speed will be low so wind resistance will be low, and friction will still be low. Nearly all of the cyclist's energy is used in overcoming gravity so weight is very important - it has to be lugged up the hill. Now, a fit cyclist who is twice as heavy as a fit skinny cyclist is unlikely to have twice the power to compensate so skinny cyclists tend to make better climbers.
How about accelerating on the flat? Well, the power-to-weight ratio of a skinny climber tends to be better than that of a bigger rider so their 'jump' could be better, but once they get up to speed they might struggle to maintain it and be reeled back in by bigger, stronger riders.
As for descending ... A big rider with more power than a small rider has a natural advantage anyway, and their gravity-assistance increases much quicker than their wind resistance with increasing size so their 'terminal velocity' is higher. I have often freewheeled past smaller riders who are pedalling like mad downhill!