Answering the narrow version, because the broad one does not have a single answer. 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.

Dr.CardioMD said:

Four weeks is the pharmacokinetics, not caution.

That is right for the weekly injectables. For the daily agents the interval logic is different and the four-week convention does not transfer.

hannah_MT said:

Four dose steps in, holding each one the full four weeks, and I am trying to work out whether the interval is a pharmacological requirement or a…

This matches mine closely enough to be worth saying so. Holding longer is the underrated move. A step that is uncomfortable at week two is frequently comfortable at week six with no change in dose, because the gastric-emptying component tachyphylaxes while the appetite effect persists. Escalating at week two throws that adaptation away.

Clinical perspective, offered as context rather than as advice.

PSA for titration users considering the 0.25mg starting dose: this dose is NOT intended for weight loss. It's a titration dose to let your body adjust. Don't be discouraged if you don't lose much in the first month.

The therapeutic dose for weight management starts at 1.7mg (semaglutide) or 5mg (tirzepatide). Be patient with the ramp-up.