Hello. Thank you for coming to JustAnswer with your question, and welcome.
Where did you hear that patients lose this amount of weight in 5 weeks?
As you are probably aware, bariatric surgery (there are a number of different types of procedures) basically causes your intake to be drastically restricted, and in some cases there is a "malabsorption" of nutrients going on as well.
Having dealt with many patients in my life who basically stop eating for various reasons, I know that 1 lb a day or more is possible even with people who have no excess calories stored (fat).
So, losing up to 80% of excess weight (which would be fat) in a year's time is not unreasonable with some people. When anyone loses that much weight however, there is also more than just fat lost. Many of these people can also have nutrient deficits, just like anyone else whose diet is too restrictive.
Generally, however, I think the more average person having this type of surgery can expect 50 to 60% of excess weight lost after a year or two. And then, some of those will regain a few pounds by the 2 to 4 year point.
As far as calories burned, you can only lose (3500 calories per lb of fat basically) the amount that your body uses (if you don't replace the calories). Some people will have fluid loses at first which account for quite a bit of weight depending on their health concerns when they have the procedure done. Fluid is very heavy. And many people who have this done are so overweight that they have other health issues, heart problems, fluid retention, etc.
In the lady's blog you posted, she went from 500 lbs to 158 in about 4 years, which would be an overall average of a little over 7 lbs per month. This is very possible. Her pictures look great (if they are real---it is a blog), and I am sure she had surgery afterward for excess skin etc. And if you look at her weight graph, the weight loss slowed down quite a bit after the first few weeks, so she probably had some fluid retention problems as a result of her normal intake and weight issues. Still....its a lot for 5 weeks.
The other site from University of Maryland Medical Center is a realistic view of the average person's results from bariatric surgery.
As far as stories on the web......well, they are stories. Everyone has one. Some will be true, many will be at least greatly exaggerated.
So again, to answer your question:
There is more than restriction of calories. There is fluid loss due to decreased intake of calories and sodium. Just being overweight can cause fluid retention. There may also be some component of malnutrition after a time, which results in your body not functioning properly.....this can also account for more loss than simple burning of calories. Severe restriction of food can cause loss of muscle tissue as well.
Yes, you are correct. Fat is basically stored calories. It does not need anything to maintain itself (calories, I mean). The cells basically shrink or get larger depending on the use of, or the storage of fat.
Of course, this is a very simplistic way to explain how weight loss works. There are other things that influence weight loss and/or gain. (metabolism, nutrients, hormones, genetics...) But it is basically correct.
There is no other way for the body to rid itself of fat. It can be surgically removed, but beyond that.....it needs to be used as energy to shrink.
And yes, I would say that the stories you read are largely exaggerated. (Who wouldn't want to exaggerate their weight loss success?) Bariatric surgery is necessary and effective for some people with extreme weight problems, but it is by no means a miracle cure. There are still issues to deal with for most people, even after massive amounts of weight have been lost. And some people I know who had it done will figure out a way to regain the weight by just eating more frequently in very small amounts.
Just FYI: here is an article about How Fat Cells Work.