While I certainly believe exercise, NEAT, not sitting, carrying water uphill, or having to walk to outside latrines contribute to health, I don’t believe on their own they significantly impact weight loss.
The body is very good at maintaining a steady state. If the body dehydrates, it will make you feel thirsty until you restore the proper water balance. If the body burns calories, it will make you feel hungry until you restore what you burned. In short, the more you move, the more you will want to eat.
People who take up running often lose weight at first, but usually gain it all back in a few weeks if nothing else changes. Runners not only want to eat more more, their bodies also get more metabolically efficient so they start to burn fewer calories for the same amount of exercise.
I believe the only way to sustainably lose weight is to change one’s diet. Shift to foods that satisfy hunger with the least amount of useable calories. Foods with lots of undigestible fiber or with complex carbs that take a long time to metabolize. This will reduce the likelihood of taking in more calories than your body wants or needs.
We all find it easy to stuff ourselves with potato chips, french fries, and pizza, eating well beyond what the body needs, but it is difficult to do the same with broccoli, carrots, and apples. There is a similar problem with meat (with respect to weight loss). There is such a concentration of calories in meat that it is easy to take in more calories than your body wants. For example, 100 gms of beef packs about 290 cals vs 190 in chicken and 76 cals in tofu.
Feeling hungry all the time is not sustainable for most people other than the most self-disciplined. The only way IMO to sustainably lose weight is to change what you eat to foods that satisfy hunger with fewer calories.
Just wanted to make the point that exercise is very important for health, but it is not sufficient for weight loss.