*a quick note, I am a biochemist, but not a doctor or dietician, so take my words with a little salt. I’m pretty sure most of this information is correct, though.
It’s all about metabolism and the body’s particular chemistry. It’s half and half true that even the experts don’t know. We know a hell of a lot, but the problem is that our bodies are amazingly complex, so there’s still a lot that we don’t know. But we do know a very large amount about the basics.
In a general sense, the things that control your weight are mostly how much energy your body extracts from food, how much it stores and in what ways, and the ways in which it goes about burning it. All of these variables interact and can effect the end result. And while it’s true that controlling for calorie intake and use can help you lose weight, it’s really not that simple in the end (which is why something like 5% of people on diets manage to keep lost weight for longer then a year or so) because all of these can shift around.
So, to start, the energy that you extract effects it, naturally. If your body is highly efficient, you will gain more calories from food, and thus need to eat less. This is the reason fiber is so often suggested for diets, as it it very hard to break down and results in our body extracting less from your food while still making you feel full. This is also why extreme calorie-restriction diets tend to work very badly, as your body goes into ‘starvation mode’ after a little while (usually a few days) and becomes far more efficient at getting nutrients from food, counteracting the effort (and making weight gain after going off the diet very, very fast).
Now, the ways in which your body stores and uses it is also highly important, as well. While the actual forms you injest are important in terms of calories vs proteins vs fat, you body is capable of inter-converting these, to an extent. It takes more energy then just using the stuff straight, naturally, but it can do it (otherwise anyone on a strict Atkins diet would die pretty fast, or at least have some really nasty side effects, as carbohydrates are the only form of energy used by your neurons). One thing that affects this heavily is insulin levels, which inform your cells as to whether to store and use energy as carbohydrates or fats. This is why diabetics tend to gain weight, as the lack of sensitivity to/lack of insulin makes it so the body is far less able to control this, and more energy is converted to fat stores. And this is also why they can go into shock from lack of sugar, as the body can’t switch over to creating carbohydrates when the blood sugar drops too low.
And of course, how you use the energy is also affects it, and this is what is usually referred to as ‘metabolism’, which is how quickly your cells use the energy. This is regulated by a whole host of factors, one common one being thyroid hormones, produced, naturally, in the thyroid. Thus, hyper- and hypo-thyroid patients (of which the latter runs in my family, actually) tend to also have great trouble regulating their weight, because while their bodies may be able to control how the energy is packaged, it’s not as capable of determining how to use it. Your ‘basal metabolic rate’ is the main thing here, which is affected by genetics and conditions such as thyroidism, as well as how active you are. More active means a higher basal metabolic rate, and so you use up more calories on average then someone else with a lower rate. Again, though, this is also affected by what you eat, so that ‘starvation mode’ affects this as well, lowering your metabolic rate to be more efficient, and thus harder to lose weight (and do much of anything).
Now, this is also only the general body chemistry in terms of food, and neurology also affects things, as @Sunny2 and @DigitalBlue has mentioned (although, do you have a source for fat cells not dying, @DigitalBlue? Not saying you’re not correct, but I haven’t heard of that, and would be interested to read up on it). The signals in your brain that tell you whether or not to be hungry or full play a huge role, and are naturally affected by your body as well (for instance, those insulin levels again affect this). However, as I am not a neurobiologist I’m not even going to attempt to explain that, as it gets even more complicated, and can get into things like upbringing, culture, and psychology. Suffice to say it’s complicated >.<.
Uh, hope this giant block of text helps!
(also, while i also find it hard to believe that really anyone is capable of taking in 15000 calories a day, very high-end athletes tend to take in massive amounts. Michael Phelps, for instance, works on around 12000 a day)