Although I generally think the study NYBiker quoted is very true, I do have mixed feelings about the message it sends to everyone. I've known too many women who lost and maintained their weight by severe calorie restriction. The people I like to refer to as "skinny fat." Back in the day, someone like this would appear in my aerobics class and it almost always ended up in disaster, sometimes bordering on medical emergency. You do need to exercise to be healthy, yes. But, exercising also helps you lose weight, especially in the beginning, if you have a lot to lose, and you are moving from unfit to fit. This doesn't count all of the mental health benefits of exercising. Yes, what you eat and portion size really do count. But, without the exercise piece, it seems like you are just putting your body into starvation mode.
For myself, I could not have lost or maintained my weight without both. When I was 25, I lost 25 pounds from changing my eating habits and beginning a moderate exercise program. It took about a year. The only other time I had to lose that much weight was after my kids were born; the first time 25 pounds and the second time 20. I was already exercising 6 days a week when my first son was born and the same when #2 was born, but I weighed 10 pounds less when I started the second pregnancy. I lost the weight both times in 4 months. I doubt I could have done that without exercising.
I've had to really cut down on my carbs and portion sizes in the past couple of years. I also can't stop exercising. What has happened is I've changed how I exercise; not just cardio, and more planned rest or active recovery. Not sure how old I'll have to be, to not care anymore... 70, 80? Since most people in my family live to their early 90s, I guess I have to keep at it for awhile.