Originally Posted by
bent-not-broken
This is not possible.
One person who "eats exactly the same" or better than when you maintained your weight and then adds exercise WILL LOSE WEIGHT! I am assuming you are saying "no more" means the same nutrional balance including calories. You will burn at least 1lb for each 100 miles of cycling you add. The comparison to others is irrelevant as YOU are not a variable.
You are eating more than you think.
The human body isn't quite that mechanical. It can and will do strange things. For example, even though you might increase exercise your body might slow down its metabolism if you aren't eating enough calories. So while you are burning calories on the bike your body may burn less calories while at rest (which is the majority of the day.)
I'm not saying this is true in the OP's case - just that the human body isn't simply an input - output machine.