As you may or may not know, in addition to being a student of physics, I worked for two summers at a weight loss camp. And so it was that I thought to apply thermodynamics to what was happening to my campers.
Some campers would lose weight steadily; others would have slow and fact points; in the long term, they all improved dramatically. And yet, when you use weight to try to measure your fitness, things tend to fall flat a little more often, and you see quirks.
As BMI measures it, I hit the "overweight" marker at 184 pounds - at which point my body fat percentage is still quite healthy. If I drop to 170 pounds (BMI 23, still in the upper half of "normal") my body fat percentage is dangerously low. I would probably drop dead before hitting the "underweight" BMI (136 pounds).
The quirk here is lean body mass. I have a relatively high lean body mass; my campers, universally, were increasing their lean body mass as well, strengthening muscles they didn't know existed, drinking plenty of water, etc. And at the most extreme end of it - you can be burning through calories and still adding just a little bit of mass as you reshape your body. I've seen it; I've also seen, on weighing day, how terribly discouraged campers get when they discovered they lost little to no weight that week.
Hidden in that news is the amazing improvements they made in their fitness. They can now hike further, lift more, swim more quickly, and they may even have lost an inch on their waistline. And when we're worried about our appearance, it's that - not the proxy of total weight - that makes the difference when people look at you.
So if you're working out hard and watching your diet, and yet you just don't seem to be losing weight, cheer up. You're still probably improving your health and appearance.