Well, the actual weight of the rider does not make much difference on the estimate of watts/kg needed to obtain a certain speed on a certain slope. This is both an adventage and a disadventage of the method, but I'll come back to this at the end of my post.
The watts needed to obtain a certain speed on a certain slope is linearly related to the weight of the object, as one can see in one of the more simplistic formula's used to estimate the watts for cyclists:
Watts = total mass * slope * speed in meters/sec * 9.8 m/sec^2
As you can see here, the estimated amount of watts covaries lineairly with the total mass of the rider + equipement. For example, if a 40kg object requires 200watts to achieve 30km/h on a certain slope, then a 20kg object would only require a 100 Watts to achieve that same speed on the same slope. However, if you now devide the watts needed by the mass, you would see that both objects require 5 watts per kg to obtain that speed on that slope. In more mathematical terms, it would look like this:
Watts = total mass * slope * speed in meters/sec * 9.8 m/sec^2
W/kg = Watts / total mass
= (total mass * slope * speed in meters/sec * 9.8 m/sec^2) / total mass
= slope * speed in meters/sec * 9.8 m/sec^2
So even if the weight varies, the estimate of watts/kg stays the same and that's why you can use a standardized weight of 70 kg in the calculations, as the actual weight drops out of the equations. This is the adventage of the method.
What's the disadventage?
Well, the method assumes that any difference in weight between riders is due to a difference of effective body mass (i.e. muscles). Imagine a rider of 100 kg going up Alp D'Huez with 10 watts/kg, producing a massive, impossible 1000 watts in a record Alp D'Huez time of 20 minutes. Now imagine the guy losing half his weight (all fat), going up Alp D'Huez equaling his record time of 20 minutes. As the weight drops out of the equation of w/kg, he has still produced 10watts/kg, but the total amount of watts is less, only 500 watts. Both performances are equal in terms of w/kg, but not in total watts produced. The second performance was worse than the first, despite the same w/kg estimate.