Hormones get over simplified sometimes. The broscience would go something like this: "If you want to get bigger, inject testosterone. If you want to get skinnier, inject leptin."
The reality is that your endocrine system is way more complicated than that, and leptin is a good example. This is an excerpt from Dr Richard Atkinson (endocrinologist):
[Leptin] is made by fat tissue, and as you get fatter, you make more
of it. That was quite a shock because everybody thought that obese
people were going to be deficient in leptin. With the more recent
understanding of leptin resistance, it makes no sense to give people
leptin if they have an impaired response. The resistance is still
there. No amount of leptin is going to overcome that resistance.
Giving leptin only helps in a few extremely rare cases in the world in
which people make no leptin at all, which causes them to overeat and
become obese. When those people received leptin by injection, they
stopped overeating and lost weight. But for the vast majority of
people, the treatment won't work, nor is leptin approved as a medical
treatment for weight loss.
In other words, the problem isn't a lack of leptin but rather an insensitivity to it (which is caused by obesity). So rather than looking to leptin to reverse obesity, obesity needs to be reversed so that leptin can function normally. From a 2007 study:
Lastly, we show that by decreasing the fat content of the mouse's
diet, leptin responsiveness of NPY/AgRP and POMC neurons recovered
simultaneously, with mice regaining normal leptin sensitivity and
Leptin does work, but you only need enough. And for folks who need it to lose weight, they have to lose weight for the leptin to work.