It's not weight, it's BMI. If you shift your composition to muscle without changing your weight, that's still a dramatic improvement. This is not "a complex." Discussions of "losing weight" are typically short hand for reducing the percentage composition of fat in the body.
If you're obese, changing composition will likely add many health benefits, and very often the overall weight of the person shifting said composition will be lower because they were carrying a lot of fat, and only added a reasonable amount of muscle if they took up exercise.
True, but the amount of people who are technically "overweight" due to high muscle mass are statistically insignificant. Even most professional athletes are in the normal BMI range; it's only a few sports or positions that rely on power where they tend to be heavier.
BMI is a perfectly fine societal tool. It is a bit less effective individually, but that’s between you are your doctor. If your doctor says your BMI is bad, it ain’t cause you’re a body builder (and for the record, body builders leaving normal BMI also increases their risks of various health problems)
Also, the vast majority of body builders are in “overweight”. Most muscle heavy gym goers should still be in normal BMI, or maybe the low end of overweight at a 10-15% body fat.
The complex people have around weight I find really strange.
I'd be surprised if most of the mental health effects don't simply follow from the realisation that you are in control of your own weight.
Feeling powerless is pretty shit.