[mapkkk]

I presume you're referring to receptor upregulation in response to the drugs. Bear in mind as you read my comment that this isn't my primary area, and it's been a while since I last studied cell biology and signalling around G-protein coupled receptors. I also have not gone out of my way to read papers about the cell signalling pertaining to these drugs, only papers around clinical outcomes for these class of drugs.

After discontinuation, most patients regain around 60-80% of the weight they've lost with the medication - but this figure is limited to the study duration, so the weight regain might have continued beyond that. A good starting point for dipping your toes into outcomes would be the STEP and SURMOUNT trials, these were the trials they did for marketing approval. (They did multiple rounds of these, I believe STEP4 and SURMOUNT4 specifically had groups that stopped therapy mid-way).

We see this rebound effect with weight loss mediated solely via lifestyle modification as well, however. Still no idea why. Very broadly speaking, only a small proportion of obese/overweight patients will manage to keep the weight off, and the rest of the patient population tends to be divided into two groups: those who regain most of it (usually around half of the lost weight will be regained within 2 years, and 80% by follow up year 5), and those who regain more weight than they had lost. There hasn't been a way to tell preemptively which group the patient will land in at the time of beginning of lifestyle modification.

On top of this, yoyo-ing is also a phenomenon we tend to see. Obese and overweight patients who've managed to lose weight once will regain, lose again and so on. This phenomenon is associated with worse outcomes than being obese alone, so it is important to do long-horizon thinking when initiating therapy (be it lifestyle or pharmacotherapy) e.g. is the patient willing to stay on pharmacotherapy indefinitely? what about an indefinite maintenance dose if the patient succeeds with lifestyle modification alone? has the patient had lost and regained significant amount of wt prior? etc.