They just has a few fat
Have you seen a thin human? Yes, of course. And does that means he doesn't have fat? No! They just have only the minimum (and healthy) amount of fat in their bodies, elves too!
In real life, there are some people with a different metabolism than another, you can note that some people can get fit easier than other, that is because of some bodies can absorb, produce and store more fats than others. Elves have a very little absorption and storage of fats on their bodies.
That fuels their mana
###That fuels their mana InsteadInstead of store excess of energy in fat, they "transmute" it in mana. Mana is just magic, it can be stored in an extremely small amount of space, in your soul, or even in another plane of existence (pocket dimension).