This is the version of the explanation I wish somebody had given me, written down before I forget what confused me. It is about the titration schedule, and it is deliberately narrow — everything I am not confident about is marked as such.
What is actually established
Four weeks is the pharmacokinetics, not caution. With a one-week half-life you need four to five half-lives to reach steady state, so at two weeks you are dosing on top of a concentration that has not finished rising. Escalating then stacks exposure and you get the side-effect burden of the higher dose before you have seen the benefit of the current one.
The condition it depends on
That is right for the weekly injectables. For the daily agents the interval logic is different and the four-week convention does not transfer.
The practical version
The arithmetic in one line: half-life about a week, so steady state at four to five weeks, so a four-week interval is one steady state per step. Two-week intervals mean every step is dosed onto a rising curve.
What I am not sure about
So the question, as narrowly as I can put it: why the interval is four weeks rather than two, and whether a slower ladder gets to the same place. If the honest answer is that nobody knows, that is a useful answer and I would rather have it.
— Dr.ObesityLA · corrections welcome and will be edited into this post with credit