Surely the drug is depressing appetite, through the action of hormones?
If you stop taking the drug to depress the appetite and then go back to not controlling your calorie intake, you’ll get fat again.
The drug triggers GLP-1 receptors that are found all around the body, but esp the pancreas. They control insulin release and sensitivty. But triggering them, you increase insulin amounts and sensitivity and thus lower blood sugar. Lower BS means more stable BS and less sugar crashes, leading to less sugar cravings.
GLP-1 also controls digestion speed. By triggering them you slow down digestion so, you are fuller for longer. It also increases leptin levels. Leptin is what tells your brain you've eaten enough for your needs. This obviously depresses appetite.
The triggering of GLP-1 receptors also supresses ghrelin production - ghrelin controls hunger and so less of it = less hunger.
In short, it causes all of those hormones to go back to 'normal' levels. It corrects what genetics and a lifetime of weight gain and yo-yo dieting have done to wreck them. It is them being so wrecked that means it iss not just 'self control' but constant and impossible battle against your own biology which is pushing you with every tool it has to eat and eat and eat until you have more than regained any weight you've lost.
So, you are right in that when you stop taking it, IF your obesity was caused by the many things that interfere with those hormones, you are likely to still have a foundational hormonal problem which will resurface. People are likely to need long term help with this.