Cycling and walking/jogging on the treadmill are very good exercises. Any cardio is good, including activities such as walking, jogging, cycling, aerobics, swimming etc. It is important to exercise between 4 and 5 times a week, for a minimum of 30 to 45 minutes each session. It is also ideal to work at a moderate to hard intensity, but for a longer duration. You should aim to do these sessions at an intensity that allows you to complete the session without feeling completely exhausted, but having worked up a good sweat and feeling that your breathing and metabolic rate are elevated.
now, with regards to weight training, it is important because lean muscle has a naturally higher metabolic rate than fat does. So, if you can increase your lean muscle mass (by weight training) then the idea is that you will also increase the metabolic rate, which means that you will, even at rest, be able to burn more energy. Hence, you will be able to keep weight off. So, that is where it fits in. However, the most important thing is to get started and to actually lose weight, you must be doing cardio training - the increase you get in metabolic rate during a 30 minute bout of cardio (and for the few hours after) far outweighs the weight training increases, and so if it's weight loss you are after, then cardio is the way to go. Once you have achieved weight loss, or you are still busy achieving it, then the weight training becomes important to sustain it.
Hope this helps
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