The simplest way to think about it is just the power/weight ratio. Let's assume a 600cc bike with 100whp and 450lb wet weight. Add a 150lb rider and we're at 600lb. To add 1hp here is 1%, so you can just take away 1% weight, which is 6lb, to arrive at the same power/weight ratio. Then you can say something like 6lb = 1hp in this case.
As another example, if you have the same 100whp but want it to accelerate like a 150whp bike (a factor of 1.5), you would just divide the weight by 1.5, and arrive at 400lb. So you would need to cut 200lb off the total bike weight.
This assumes that there's negligible wind resistance (ie low speeds) but there's no way you can make a rule like this that would apply the same at different speeds. If you assume there's some wind resistance negating the effect of power/weight ratio, you could raise the 6lb figure I calculated above higher to say 7lb like you guys mentioned earlier. Cutting weight couldn't make you go to a higher top speed, it just scales acceleration.
All these kind of estimates are made to apply only to a typical bike with typical specs. For example, obviously a bike with 1hp and 500lb wouldn't gain another "1hp" or doubling its power/weight by cutting just 7lb.
Just think of it as a simple ratio between power and weight. Put an extra 1% to power or take away 1% from weight, you'll get the same effect with this simplified analysis that doesn't take drag into account.
