Accepted answer
The part that matters: 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.
The maintenance question turns on what you are maintaining. If the objective is weight maintenance, the withdrawal-extension data suggests that a fraction of the therapeutic dose retains a substantial fraction of the effect. If the objective is the cardiovascular or renal endpoint, the trials that demonstrated those endpoints used the full dose, and extrapolating downward is not supported by anything.
The label instructions for a missed weekly dose differ between agents, and reading the actual prescribing information rather than a summary is worth the ten minutes — the thresholds are specific and the reasoning behind them is stated.
The limitation of all trial-derived dosing reasoning is that trial populations were selected, monitored and supported in ways that do not resemble anyone reading this.
The short version: four-week steps because that is steady state, and the ladder is about the side effects, not the result.