Taking the question as asked, rather than the general version of it. 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.

If somebody has the primary source to hand I would rather cite it than paraphrase it.

LabKate 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.

Dr.PulmRoch said:

I titrated faster than the label because I felt fine, hit a wall at the third step, and had to come back down — which I now think was the predictable…

Same position here, arrived at the long way round. 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.

Happy to go further on any of that.

Adding the clinical framing, because it changes how the question reads.

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.