Putting this up for argument rather than for agreement. I have read it twice and I am still not certain what it supports.
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 subgroup findings are the part I trust least — with enough subgroups something is always significant, and these were not all pre-registered.
What I actually want to know is which effects tachyphylax and which persist, because the answer explains why tolerability improves while the appetite effect keeps working. Practical detail welcome, however dull — the duller the better.
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.