Be patient!! Rapid weight loss is water and muscle (think Atkins). You don't want to lose your precious muscle because it is a fuel burning machine, whereas fat just sits around & goes along for the ride (literally!). Atkins restricts carbs. Carbs retain water. Start eating carbs and guess what!!
More important is your body composition - fat to lean body weight ratio. Muscle weights more than fat. If you look at a body builder, she will register as "obese" in the charts because of the height/weight schedule.
I would augment cycling with hitting the gym. You want compound exercises - those that work many muscle groups at once. Squats, bench presses, overhead presses and pull ups are examples. Get a good book or get a trainer so you don't get hurt. Building muscle will help your cycling too.
A good website is:http://www.stumptuous.com/weights.html
Good luck!