I think you are getting confused between weight loss and fat loss.
Per volume (however you want to measure it, cubic inch, cc, whatever) fat weighs less than muscle.
So let's assume that you somehow manage to, between weigh-ins, you manage to lose 1 lb of fat, and gain 1 lb of muscle.
You are right where you started, and achieved nothing, right?
No wrong. You are going to be smaller, as the 1 lb of muscle takes up less space than the lb of fat did, and you are raising you base metabolic rate (it takes more energy to maintain 1 lb of muscle than it does to maintain 1 lb of fat.
So if you were to keep this up, the exercise actually helps you lose weight. As your body becomes more toned, the weight loss increases.
If you want to read more about this, I would recommend the book Fit or fat by Covert Bailey. Good read, and it goes into the bio chemistry of how your cells use various sources of energy.

Myself, I ride 2-3 times during the week, 45-90 minutes and on weekends 30-50 miles on both Sat and Sunday. A few weeks back I rode 60 miles one Saturday to celebrate my 60th birthday. I will do a century ride this year.
One last thing, don't forget Dr. Atkins said in his book "If you aren't exercising, you aren't doing Atkins."