Accepted answer
Four weeks is not a magic number, it is approximately five half-lives, which is the interval over which a weekly compound reaches steady state after a dose change. Escalating faster means escalating onto a rising concentration.
Holding at a step for longer than four weeks before escalating does appear to reduce cumulative gastrointestinal burden, which is unsurprising given that adverse events cluster in the one to two weeks after each increase. What it does not do is change where you end up, provided you get there.
The argument against splitting a weekly dose is arithmetic rather than ideological. Peak-to-trough ratio for a seven-day half-life compound dosed weekly is about two. Split it into twice-weekly and the ratio falls to roughly 1.4. That is a real reduction in fluctuation and a negligible one in absolute terms, and you have doubled the number of stopper piercings and the number of small-volume measurements, each of which carries its own error.
The pharmacokinetics of the acylated agonists are well described: absorption from the subcutaneous depot is slow and rate-limiting, the elimination half-life is approximately one week, and steady state is reached in four to five weeks. Every dosing question in this section follows from those three facts.
Worth noting that inter-individual variability in exposure at a given dose is substantial, which is why the ladder exists rather than a single population dose.
The short version: four-week steps because that is steady state, and the ladder is about the side effects, not the result.