I lost 75lbs about 25 years ago. I rarely do strict keto since then, but have greatly reduced carbs overall. When strict, I can't eat enough to gain, and always lose. The "calories in must be less than calories burnt" mentality is completely contrary to my experience.
I have known others who were not as successful on keto, but I'm sure it comes down to hormones. For those (like me) who are insulin dominant, keto just works. For those who aren't, it isn't nearly as helpful.
(The following is a TLDR agreement to the above.
BLUF:
You are correct. meta-studies reinforce your experiences across ages, genders, and body types.
A couple of factors come into play.
When you cut out carbs, your calories have to come from either protein, fats, or a combination of the two. Both protein and fat take longer and more work to digest than carbs, so they are both more satiating than carbs. You feel fuller quicker and longer eating fats and proteins than eating carbs. What that means is that you may feel like you're eating more at your meals, but you are probably eating less snacks through the day. I've seen a lot of people on low/no carb that think they are eating more calories, but over the day/week, they are not. And as stated earlier, some of those eaten fat/protein calories are not burned. They are passed by the body in some way. (Example, with a lack of carbs in the bloodstream for energy, the body converts fat into ketones, and burns them for immediate fuel. That's why the low carb works--and cleans up the bloodwork heart-health numbers, by the way. Whereas unused carbs in the bloodstream get stored as fat, unused ketones exit through the ol' pee-stream. So, literally, the adage that you have to burn more calories than you eat is one of those generally-true-but-not-exactly statements.)
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Especially if you want to work out and diet to reshape yourselves, find an old copy of "The TNT Diet" by Men's Health. Men's Health is NOT a good place to blindly follow, as they publish all kinds of plans from all kinds of folks, with all kinds of competing paradigms. But this one is solid. The scientific meta-studies are all in there, along with a detailed plan. It's why, what and how. If you can't find that, look for an open-source electronic copy of either "The Metabolic Diet"
https://metabolicdiet.com/diets/the-metabolic-diet or its alternate name "The Anabolic Diet", which is the same principles, but came earlier with fewer meta-studies to prove the concepts. Note that both plans are much more effective with resistance training,
and specifically recommend full body workouts. The reasons are in the books. Basically, full body resistance training works all the big muscles, burns more energy, and creates a heavier recovery load post-workout, which effectively raises the metabolism for a couple of days as the body puts energy into repairing those big muscle groups.
Also, after a month or so of no-carb to start, depending on your goals and personal needs, they move you to a carb cycling mode where you go no-carb for 5-6 days, and eat carbs 1-2 days a week. This flips some muscle-gain hormonal switches in the body that helps with muscle gain, whereas strict no-carb all the time decreases muscle-gaining hormonal response in the body. An added benefit is that these plans don't deprive you of carbs. They just get you to postpone them. It's been my experience that it makes no-carb life easier. I can tell myself that I'm not depriving myself, just postponing. Also, carbo-HYDRATES hydrate. Another benefit of carb cycling is, when you spend a day carbing up while gaining muscle, the carbo-
hydrating swells the muscles and you look better for a couple of days. lol
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Also, not sure I've seen it mentioned. If you are adding resistance training to diet (and you should), don't judge progress by weight. Muscle weighs more than fat. So as you lose fat and gain muscle, you may actually even GAIN weight while losing waistline. Change your eating habits. Give yourself some strain and sweat several times a week. Get plenty of sleep. Hydrate. Even if you don't go low/no carb, cut out stupid-calories like sodas, refined carbs, sugars... (Look into Glycemic Index/Glycemic Load diets if you don't think you can do no-carb. Slow-carb (low-GI) is also very good and super-healthy.)