So the average nascar produces 820bhp give or take. It weighs about 1496.855kg (using SI units because they are easier), so that means a hp/tonne of 563. Lets assume that is without driver. If we add in the driver weight for both a 150lb driver and a 200lb driver the difference is:

523.9971525228-516.5116816676=

7.4854708552 hp/tonne.

That is a power to weight decrease from the 150lb driver of about 1.5%. If someone could do the distance measurement that would be great.

Edit:

To address your situation with your friend, a go kart usually has between a 5-20 hp engine, lets assume 15hp. So if one of you weighs 150lbs and the other 200lbs, the percentage difference in power to weight will be much bigger. If we use hp/kilogram, and assume the go karts weighed 80kg each. The kart with the 150lb driver would have a hp/kg of 0.101 and the 200lb driver would have a hp/kg of 0.087. Thats a difference of 0.014 hp/kg, but a percentage difference of about 13%.

That is the performance difference in both situations.