Accepted answer
Stated carefully, 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.
Where the label ladders differ between agents, the differences track the potency ratio and the tolerability profile rather than anything deeper. It is worth reading the ladders side by side once, because the pattern — small starting dose, four-week steps, a defined maintenance range and a defined maximum — is identical in structure across the class.
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 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.
One qualification — this is protocol arithmetic and reported practice, not a recommendation. The compounds in question are not approved for human use when supplied for research.
Read the actual prescribing information for the agent in question. It is short, specific, and more reliable than any summary of it.