What are the benefits of yoga, and can it help with weight loss?

Most people associate yoga with the postures, and many people think they can't do yoga, because they aren't flexible. Yoga is about becoming more flexible, just as practicing tennis helps you learn to eventually hit the ball.
We call it "yoga practice" because it is progressive; there is always more to learn, and the body continues to transform as the practice continues. A yoga practice doesn't become boring or tiresome, if we are practicing awareness along with alignment. In fact, it is this awareness that carries over into our life off the mat. Yogi Desai would say "The physical benefits of yoga are simply side effects of your yoga practice" because it is the inner work of yoga that brings unity to body, mind and spirit. But, because you are working in new ways with your body, I will begin with the physical benefits, which will encourage you to continue your practice on the mat!
While yoga is never considered a cure for ailments, many people have astounding results with regular practice. I believe it is safe to say that any gentle, regular yoga asana practice will improve your physical health to some degree.

The internal massage of all organs, glands, and systems of the body results in the following benefits:
Digestion and elimination improve; organs and glands do their work more efficiently, resulting in release of toxins and de-stressed muscles; increased blood circulation, and more oxygen in the blood increase energy.
Pressing into the floor stimulates bone growth and can decrease risk of osteoporosis.
Muscular strength and flexibility increase, helping prevent injuries.
Balance improves.
Deep breathing releases stress, increases lung capacity, and energizes the body while calming the mind. Breathing exercises can relieve asthma if done daily.
Yoga asana practice can relieve low back pain, sometimes immediately. Inverted postures such as Shoulder Stand, even the modified versions, can lower blood pressure. Gentle twists can realign the spine. Postures that squeeze the upper back and stretch the neck can relieve headaches.
Many people find that their sleep improves with yoga practice.

The inner benefits of a regular yoga practice usually appear first in regard to temperment. As the student learns to slow the breath down and to be more aware of feelings, it becomes more natural to breathe, relax, feel, watch and allow off the mat. So, instead of reacting habitually in certain situations, you begin to respond consciously because you are training yourself to control the mind rather than "flying off the handle" as you used to do. You may notice that as you are stopped by a red light you choose consciously to breathe slowly until the light changes, instead of choosing unconsciously to become anxious or angry. If someone pulls out in front of you, you switch from fear or anger almost immediately into calmly focusing on your driving, and realize we all make mistakes.
Moms become more patient with their children; spouses become more patient with each other; and we become more patient and forgiving with ourselves.

It is at this point that you can begin to realize how yoga practice can affect weight loss. As we become more conscious of what we are doing and how we are being off the mat, we become more conscious of how and what we are eating. (Sorry if you were expecting a magic posture or two to cause you to lose weight!)
Sitting down to a meal, we can gaze at a plate of food, smell the fragrances, and become conscious of what we are about to do: put life-sustaining food into our body! Then we proceed to eat consciously, chewing each mouthful thoroughly before swallowing. Chewing thoroughly has the added benefit of causing us to be satisfied with less food! Try chewing each mouthful 40 chews before swallowing, and see what happens!
A "yogic" diet consists of as many natural, unprocessed foods as possible; eating only until the stomach is 3/4 full and then stopping for at least 2 hours; eating only when hungry (not "craving"); and drinking water and/or taking long, deep breaths to ward off cravings.

As your asana practice improves your well-being and increases your flexibility, you will feel more like getting out for a daily walk or jog, taking part in a sport, or putting on some music and dancing. In other words, you'll feel more like moving. Acknowledging that the best method of losing weight is eating healthier and moving more, voila! yoga helps with weight loss!