One simple way to estimate it is to calculate whatever preserves the power to weight ratio.
For example, suppose you have a 3600 lb. car with 300 horsepower. That's 12 lbs. per horsepower. Now you (somehow) make the car 200 lbs. lighter. It now has 11.3 lbs. per horsepower. If you stayed at 3600 lbs. you'd need (3600 / 11.3) = 319 horsepower, or 19 extra horsepower, to maintain the same P/W ratio.
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