Basically, you gain 1% in running speed for every 1% reduction in body fat. To put this in perspective, if you currently run a 10 K at a pace of eight minutes (8:00) per mile, losing 5% of your excess body fat will improve your time to 7:36 per mile (8:00 x 0.05 = 24 seconds faster; 8:00 - 0:24 = 7:36). Consequently, you will run the 10K about 2.5 minutes faster, and your marathon about 11 minutes faster. - Training to Improve Your Running Ability by Mel Williams, PhD
MY COMMENT: So lets say you weigh 150 pounds and are 15% fat (22.5 lbs of blubber). If you lost 5% as in Williams example, that would take you to 10%,(so now you carry 15 lbs of the stuff). You've dropped 7.5 pounds.
Another theory on body weight and running performance was offered up by Tom Osler, who believes every extra pound of flab cost you 2.5 seconds per mile .
Back to the example by Williams, a 7.5 pound drop in fat weight means you'll run 24 seconds per mile faster. Using Osler's theory, you will run just under 19 seconds per mile faster.
The formula mentioned by Williams is based on "oxygen consumption dynamics" measured in a lab, while Osler reviewed data from actual runners and their performances.
Remember- you can also go too low with your body fat percentage! Skinny world class male distance runners can be as low as 4-5%, but most of us carry more fat cells than they do and find it near impossible to get below 15%. You won't run well on a starvation diet either.