Collecting this in one place because it comes up every few weeks and the answer is always assembled from scratch. 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
One condition: holding indefinitely at a dose that is not doing anything is not patience, it is a stall with a nice name. The distinction is whether appetite has changed at all at the current step.
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
What I am trying to establish is why the interval is four weeks rather than two, and whether a slower ladder gets to the same place. Practical detail welcome, however dull — the duller the better.
— Dr.ObesityLA · corrections welcome and will be edited into this post with credit