To GOLFPRO's point, when I started loosing some belly fat and just becoming overall healthier I noticed a little drop in my score. Obviously getting out and playing more and maybe getting some instruction will be the biggest way to lower your score, but becoming more flexible and looser will help. I was a point where my gut was "getting in the way" and I noticed that it was harder to lead with my hip and really drive the ball.
Since losing some weight and lowering my body fat, that has all become easier. When I was "fat" my average full round was about 115-120 - that was 2 years ago. Last summer I golfed as much as I did 2 years ago and only broke 100 a couple times and was averaging around 95. Neither are great, but losing some weight, getting stronger by lifting and adding running/swimming seemed to help me.
It'll be interesting to see what this summer brings.