What is leptin? Discovered in 1994, leptin is a hormone that signals the availability of energy reserves in the body. "High leptin levels are interpreted by the brain that energy reserves are high, whereas low leptin levels indicate that energy reserves are low", the latter causing the body to enter a resource-minimizing starvation mode [1]. More recently, leptin has also been shown to regulate "neuroendocrine and immune function and [play] a role in development" [2].
Why is leptin so important to obesity? "Most obesity occurs in the presence of increased leptin levels", which suggests a form of "leptin resistance" in obese individuals [2].
Leptin changes our understanding of body fat, also called adipose tissue. We generally think of body fat as simply stored energy reserves, so fat can be burned by decreasing our caloric intake (diet) and increasing our energy usage (exercise), forcing our body to dip into its reserves. This approach is generally referred to the calorie-in/calorie-out (CICO) model. While true to an extent, this perspective is too simplistic, given one key fact: leptin is primarily produced in adipose tissue [1]. This fact means body fat is actually an endocrine system organ.
Consider this: an obese individual has elevated leptin levels. A decrease in adipose tissue causes a decrease in their leptin production. Due to leptin resistance, low leptin levels causes the body to enter starvation mode, and hardcore dieting causes leptin levels to drop further, which makes weight loss even more difficult. What they mean by "metabolic adaptation" may be understood as "leptin adaptation", though I'm just speculating there.
It's strange that so many articles talk about weight loss and "metabolism adaptation" without mentioning the hormone signalling energy availability. With leptin, we clearly see the body has an energy availability feedback loop, and fighting the intrinsic dynamics of a feedback loop rarely leads to good outcomes.
On this vein, I want to highlight slothtrap's comments:
>The more frequent the dieting and steeper the caloric deficit, the worse metabolic adaptation gets, and the longer it takes to return to normal.
>I wonder if those who sustained higher levels of exercise were actually in a steeper caloric deficit.
>perhaps it's fair to say that if you're going to exercise, you best sustain it.
These comments align with present understanding of leptin dynamics. A steep caloric deficit pushes the obese body into starvation mode, so net energy expenditure from high levels of exercise will be decreased. Weight loss will be maintained once the body adjusts its leptin production and usage, which, as of now, can only be accomplished with habit.
It's also worth mentioning here the hormone ghrelin, which was identified in 1999 and is nicknamed the "hunger hormone" [3].
[1] https://en.wikipedia.org/wiki/Leptin
[2] DOI: 10.1146/annurev.physiol.62.1.413