The relevant detail is that 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.
Escalating in response to a plateau is a specific and common error of reasoning. A plateau after four to six months is the expected trajectory in every trial in the class — the curve flattens because energy expenditure falls with mass, not because the receptor stopped working. A dose step may still be reasonable; "the loss stopped" is not by itself the reason.
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".
Read the actual prescribing information for the agent in question. It is short, specific, and more reliable than any summary of it.
edited 11 Sept 2024 by h_villanueva — added the method parameters