Somehow it feels like horsepower has a greater influence on PP than weight, obviously because horsepower will always means higher speed and better accelerations at higher speed, but it won't really efficiently describe performance on very low speed raceways like eifel kart or autumn ring mini.
I also noticed some cars have better "base" PP than other cars with the same horsepower/weight ratio, but I don't really know how one can properly calculate cornering performance, since it depends of vertical and horizontal center of gravity, car length, the size of tires (type of tire has nothing to do with PP), stability in corners, suspension, etc: any car will perform differently.
I guess it's of the form
((horsepower^constant1)/weight)*constant2 + constant3.
constant1 being between 1.2 and 2.
Oddly, I also noticed increased power on very PP cars does not increase PP so much.
The other thing, I don't think PP precisely describes the exact potential for a car to outperform other same-PP cars on the same raceway, since weight will play a more important factor on slower tracks than faster ones, especially with comfort and sport tires.
What I'd love to know for sure, is how to rate certain tracks for either speed or slow cornering, so I can choose car for the same PP limit, either a lighter or more powerful car.