In theory it's pretty simple, for a given input of power, speed will be directly proportional to all up weight (rider+bike). Assuming that friction (air and road) remains constant between the two. So if you are putting out 200W, and you plus bike == 100kg, then you will have a speed of x, if you plus bike =80kg and you're putting out 200w, then your speed will be proportionally greater than x.

Where this becomes more complex tho is that aero drag represents a far bigger factor about your speed than bike weight. I often see Dutch bikes with clip on aero bars. They may weigh 25kg, with a 80kg Dutchman on, but in the Omnidirectional headwind, those bars make a significant difference. It's also worth noting that aero drag effects things based on a cube root or some such (no doubt Kim will be long shortly to correct me), so an improvement in your frontal area by x, will have a much more significant impact as a proportion, than a similar change in weight...

Weight (okay, mass, but we'll assume constant gravity

) has several effects:

1) It slows you down going uphill

2) Rolling resistance increases in direct proportion to weight

3) There's the noted effect on acceleration

4) If your pedalling style involves throwing the bike about, the weight of the bike acts as a damper on this.

The power required to ascend against gravity is proportional to your rate of vertical ascent (plus a constant for not rolling down the hill).

The power required to overcome rolling resistance is proportional to speed (at least for the region that bike tyres are designed to be used in).

The power required to overcome air resistance is proportional to the cube of airspeed.

What the latter point means is that when you're riding up any significant gradient, your air drag falls to virtually nothing and you're basically fighting gravity plus a bit of rolling resistance. I heard a talk once from a bigwig in BC who said that Chris Froome is 95% fighting gravity on any alpine climb. When I re-ran the calculation for my friend riding up a pass on holiday last year, it was more like 99% - because we were going at half of Froome's speed so air drag was even lower.

There are several ways in which bike weight will have a

bigger effect on a club rider than on Chris Froome:

1) Being 99% rather than 95% of their resistance going uphill means that there's a proportional gain there

2a) Because they are travelling slowly and air resistance is less, rolling resistance will be a larger portion of their overall resistance, so the proportional increase due to greater weight will have a greater effect on them.

2b) The club rider is likely to be running heavier tyres than Chris, so the proportional increase in rolling resistance will again have a greater effect on them.