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.
Extending the interval and reducing the dose are not equivalent manoeuvres. Reducing the dose lowers the whole concentration-time curve proportionally. Extending the interval lowers the average but deepens the trough, and for a compound whose effect on appetite tracks concentration, a deep trough is felt.
Specifically, 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.
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".
The short version: four-week steps because that is steady state, and the ladder is about the side effects, not the result.