Posting this because the summary going around does not say what the paper says, and the difference matters for how people here are using it.
The mechanism is more central than most summaries suggest. Receptor agonism in the arcuate nucleus activates POMC neurons and inhibits AgRP/NPY signalling, and the downstream MC4R pathway is the same one disrupted in monogenic obesity — convergent genetic evidence that the target is the right one. Peripherally there is glucose-dependent insulin secretion, glucagon suppression and delayed gastric emptying, but the gastric component largely adapts over months while the central effect persists, which is why the durable effect is appetite rather than fullness.
Where I think it is weakest: the follow-up is short relative to how long people actually take these drugs, so durability is an assumption here rather than a finding.
The question I want answered is which effects tachyphylax and which persist, because the answer explains why tolerability improves while the appetite effect keeps working. Happy to be told the question itself is wrong.
Note on sourcing:
Figures above are from the primary publication rather than the press summary. If a number here disagrees with one you have, post yours and we will work out which of us is reading a secondary source.