A reference post rather than a discussion. Corrections are the point; I would rather this be right than mine. 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 pharmacokinetics explain nearly every practical question asked here. Albumin binding above 99% slows clearance enough to make weekly dosing possible; a terminal half-life near a week means four to five weeks to steady state and therefore a four-week titration interval; subcutaneous bioavailability around 89% means injection site barely matters. Those three facts answer most timing questions before they are asked.
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. If the honest answer is that nobody knows, that is a useful answer and I would rather have it.
— SkepticalSean · corrections welcome and will be edited into this post with credit