In practice, 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.
Steady state, worked: with a half-life of about seven days and weekly administration, the accumulation ratio is roughly 1/(1 − 0.5) = 2, and you get to within about 97 per cent of steady state after five half-lives, so around thirty-five days — five weeks — after any dose change. A four-week step interval therefore has you escalating at roughly 94 per cent of the previous dose’s steady state, which is close enough to be sensible and not so close as to be conservative.
It helps to be literal here: missing a dose by three days on a weekly schedule takes the trough down by less than a factor of 1.35, which is well inside the variation you would see between two on-time weeks. Missing it by five or more days is where the label instructions start to differ between agents, and the reason is how close the next scheduled dose is rather than any mechanistic threshold.
SURMOUNT-4 is the withdrawal trial to read on the maintenance question: after an open-label lead-in, randomised withdrawal produced substantial regain in the placebo arm while continued treatment produced continued loss. It is the cleanest available answer to "what happens if I stop".
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.