Except....practically everyone here talking about how they lost weight is also talking about their exercise regimen. Well, the simple physics also shows that exercise has nothing to do with weight loss.
That's far too simplistic. If you do more exercise you burn more calories. That's a fact.
From a mathematical point of view it's simple. To lose "weight" you need to burn more calories than you eat.
From a real life point of view, the human body is an incredible machine, and it wants to stay in homeostasis. Meaning that if you take a 1 sided approach to losing weight, the body will compensate for it in the effort to stay the same.
So if you just sit there and simply eat less, the body will start to lower your metabolism to compensate for the missing calories. If you keep eating even less, the body will start to eat away at it's own proteins (muscle tissue and eventually internal organs) BEFORE it starts eating away at the fat.
This is killer, because the more muscle you have, the faster your metabolism is, and if you lose it, you're hurting your body's capacity to burn fat.
This is why exercise is an important part. It accelerates fat loss simply by burning calories, but at the same time forces the person to use their muscles, and switches the body into a muscle sparing mode (It figures you need the muscle because you're using it, so it is forced to start burning fat instead)
Cardio will work out your legs, but you need to work out your upper body also, and this is where weight lifting comes in.