Weight is for resistance muscle training. Bicycles are for aerobic (cardio) muscle training. You can ride a heavier bike, but you won't be as fast up a hill as a person of equal physical condition nor will you accelerate as fast.
So when your equal on the lighter bike is beating you at all you do, the fun will go out of riding and you won't do it as much.
Besides, you can expend just as much energy on a light bike. And it's all positive in that you'll be faster up a hill and go further on a tank of gas (stored energy in your body).