Collecting this in one place because it comes up every few weeks and the answer is always assembled from scratch. It is about the pharmacology, and it is deliberately narrow — everything I am not confident about is marked as such.
What is actually established
The mechanism is more central than most summaries suggest. Receptor agonism in the arcuate nucleus activates POMC neurons and inhibits AgRP/NPY signalling, and the downstream MC4R pathway is the same one disrupted in monogenic obesity — convergent genetic evidence that the target is the right one. Peripherally there is glucose-dependent insulin secretion, glucagon suppression and delayed gastric emptying, but the gastric component largely adapts over months while the central effect persists, which is why the durable effect is appetite rather than fullness.
The condition it depends on
The adaptation point cuts both ways: tachyphylaxis to gastric emptying is why tolerability improves, and it is also why people who were relying on physical fullness feel the effect fade while the appetite effect is still working.
The practical version
Numbers worth memorising for this class: Tmax one to three days for the weekly peptides, terminal half-life about a week for semaglutide and about five days for tirzepatide, steady state at four to five half-lives, subcutaneous bioavailability high enough that site choice is irrelevant.
What I am not sure about
The narrow version of the question is which effects tachyphylax and which persist, because the answer explains why tolerability improves while the appetite effect keeps working. Happy to be told the question itself is wrong.
— hannah_MT · corrections welcome and will be edited into this post with credit