Think about it logically. Look at how many calories are required for a larger person to simply maintain their weight - and ask yourself where this number comes from.
Calories are quantities of energy, and hence the 'maintenance calories' are the amount of energy required to just get by at that same weight. Now, everything our body does requires energy - pumping blood around the body, creating enough heat to keep the body's temperature up, powering the brain, filtering blood in the kidneys, liver function, digesting food...the list goes on.
Now think how much bigger the scale is if one person is twice the weight of the other - look how much more body mass there is to keep at a constant temperature, how many more cells there are in the whole body which need a supply of blood. Look how much more energy it would take in order to simply lift up an arm - and you can see that for weight loss, the average larger individual has the advantage because everything they do requires more energy than could be said of the average smaller person (we will, for now, ignore muscle mass as a factor).
To simplify weight loss...Fat is a store of energy, in essence a food, which can be measured in terms of calories much in the same way as the food in the refrigerator. 1 pound of fat contains approximately 3500 calories of energy, and hence if you don't feed your body enough food, it will use the food (fat) which it has stored for itself in order to power the body for the day. If this happens over a prolonged period, the body's fat store will reduce and the body will become lighter. Think of your body fat as an extra little refrigerator inside you.
Now take Kara's earlier point - if you want to lose 1lb of fat, you have to sacrifice 3500 calories of food (or exercise more!) so that the body will use its own supply. If you like, cut out 500 per day and in a week you will have lost a pound. A person who wants to lose 2lb per week sacrifices 1000 calories per day and so on. But is it really possible to cut out 1000 calories per day if your body is only using 1600 to live on? Not likely.
However - and this is controversial - for a person who requires 4000 per day, a 1000 loss is not that much of a hit. Put it this way - if you eat a lot of junk food and have a terrible diet totalling 4000 calories per day, including 4 cans of Coke, following this mathematical approach to weight loss means that simply switching those 4 Cokes to diet Coke will lose at a rate of over 1lb a week initially. You could even keep the rest of the diet the same!
The much smaller person just has a lot less to cut out of their daily intake whilst still getting the required nutrients.
[disclaimer: I do not represent Coca-Cola nor do I recommend this approach to weight-loss!]