My wife is overweight, and I (as someone who works as a researcher into an unrelated area of diabetes) had a look at what it does and whether it might be helpful for her.

Semaglutide appears to have two main methods by which is works. Firstly, it increases the production of insulin, and secondly it makes you eat less.

Drugs that increase the production of insulin are typically prescribed for type 2 diabetes (which is a disease strongly linked with excess weight). However, in a lot of ways they are the exact opposite to what you want. With excess weight and type 2 diabetes, the immediate problem that the doctors are trying to treat is that you have too much sugar in your blood. Increasing insulin helps temporarily because it causes various cells around the body to pull sugar out of the bloodstream and store it in an alternative form. This includes fat cells. However, in the case of excess weight or type 2 diabetes, these cells are already full, and the body is effectively having to use higher and higher amounts of insulin to cram all that circulating sugar away. Adding more insulin causes further increases in weight and makes the problem worse in the long term. The problem isn't too little insulin - the problem is too much blood sugar, exacerbated by the fact that all the very full cells are reluctant to soak it up.

For this reason, not eating is extremely effective at fixing excess weight and type 2 diabetes. Since the problem is too much blood sugar, reducing the amount of sugar that we shove into the blood from our food is the right way to treat it. However, diets are difficult. The keto diet is great, but it's hard to stick to effectively, unless you absolutely love it and make a habit of it. The urge to eat a little bit more than you should or the wrong thing is extremely difficult to shake, and it's hard to get the right portion sizes in some societal setups. It can actually be easier to do fasting. That way you have set yourself a very simple rule to stick to, and it's completely obvious what breaks the rule. Don't worry, you won't starve if you have more than a small amount of body fat. Humans can survive for an extraordinarily long amount of time without food. The current record is 392 days[0]. The other great thing is after a couple of days you don't really feel hungry any more, and all sorts of other health benefits cut in. Willpower becomes much less of a problem than with restrictive dieting. There isn't any harm with not eating for a couple of days in a row every few weeks. I'd definitely consult with a doctor if you plan to fast for longer, but make it clear to the doctor that you're doing this and you want support to do it safely, not that you are open to being persuaded out of it.

Fasting is a scary thing to many people, including doctors, so you'll often get them tell you you're crazy or advise against it, but there's no reason for that. People have been fasting for all sorts of reasons, including religious, for millennia, without any serious problems.

Not eating is the single most effective treatment for type 2 diabetes. There are multiple people who have been diagnosed with type 2, and then after just a few days of fasting no longer have it. My conclusion having looked at Semaglutide was that it might help treat type 2 diabetes, but it'd only do that really by making you eat less because you feel like crap, and it has all sorts of other bad effects as well, so it'd be better to eat less while not feeling like crap instead.

So, my wife has had a few rounds of fasting about a week or two at a time. That anecdote shows about an average of a pound weight loss per day with no exercise, and the weight has stayed off. I have heard other people say that the weight tends to stay off after fasting when it wouldn't after just dieting.

[0] https://en.wikipedia.org/wiki/Angus_Barbieri%27s_fast