Well for an extreme comparison, a Harley has in the vicinity of 60-80hp depending on size, but weighs between 500-800 lbs + rider. Then you have sport bikes which can have around 120hp and only weigh around 400lbs + rider. Pretty quick aren't they? So no you're not really increasing your HP by decreasing your weight just the ratio, UNLESS you're talking about decreasing the weight of drivetrain components and increasing BHP then yeah that's correct.
1984 318i 5-spd that's not currently registered... project car.
1998 Subaru Legacy Sedan
1996 Nissan Maxima is the girlfriend's car that was glad to meet somebody who knew what "routine maintenance" was.