Same for the situps and pushups I've been doing since August. I'm a hell of a lot more fit than I was, and I move better than I have in years. Hasn't made my gut any smaller. Sure, I've had to put three new holes in my belt, and probably need to go down a waist size next time I buy trousers. But it turns out that improved abdominal muscle tone just means you carry belly fat higher, so even though my waistline's shrunk, I actually look fatter than I did before. (On the other hand, I can move like I did in my twenties, so I'm willing to take the hit to my narcissism here.)
I've twice in the last decade lost fifty pounds or more in under a year. Both times, I did it purely by means of calorie restriction.
Exercise will make you healthier. It will not, by itself, make you lose weight. You do that by making sure that (calories in - calories out) has a negative sign, daily, over a long period of time. Aerobic exercise can help in that you burn more calories that way. But it's an adjunct, and insufficient on its own.
It's not easy, especially when you start out habituated to large meals and highly caloric sugary foods. It is absolutely doable, and the younger you start, the easier it is.
Put another way, if you ran fifty miles and took in no calories (obviously hypothetical), you'd lose ~1.5 pounds. You still have to make dietary changes if you want to lose weight.
Signed, Skinny, lifelong runner who hasn't the first clue what it's like to try and lose weight