Don't know if things have changed, but ...
As a 1st Lt, i had a 19-year Master Sgt working for me, By all appearances, he was WAY over the max weight limit.
My commander was always on him about it, but there wasn't much we could do. That commander would make comments around others like, "How does he keep those shirt buttons on? Titanium thread?"
The solution for the shirt buttons bulging was me telling him to go buy larger shirts.

He did, and that helped him at least look less like he's bulging out of his uniform.
;I looked through his personnel file, and he was either evaluated for his weight at the hospital or on the official weight management program almost all of his 19 years in service.
The last eval he had by an AF doctor told him, "You're just a big guy. i've seen way worse in uniform." The result was the Sgt's max weight limit was increased to 5 lbs over his current weight.
Over his career, the weight limit was increased no fewer than 6 times. He was my height, so his max was in the 192 lbs range (it varied over the years, but no more than 195). I was 175.
By the time he retired at 20 years, his max weight had been pushed to 238 lbs. What I noticed was, every time his weigh limit was increased, he met, and soon after exceeded, his new max. It was as if he saw that as a challenge to exceed rather than a reprieve from the current harassment over his weight.
I wound up counseling him 6 months before he was up for reenlistment. I asked if he expected to remain in the AF, and he said he'd like that option when the time to retire came. I told him i needed to see improvements in his appearance, compliance with his weight standard, and in the example he set for our more junior enlisted. At the time we had a TSgt, a SSgt, and an A1C (Airman 1st Class) working in the section. He was my NCO, and I needed him to provide guidance -- not be a poster boy for what not to be like.
After 6 months, I declined to recommend he remain on active duty after he reached retirement. When I told him that's what I was going to turn in, he said he didn't blame me. I gave him a chance, and he failed to follow through. I did make sure his retirement pay would not be impacted since his separation date was 2 months before his 20 year retirement date. Regulations were that, when the separation date is within 12 months of being able to retire, his separation date would be adjusted to coincide with the 20 year mark.
In summary, that was in the 1980s. So, this all started with him joining in the 1960s. Overweight military members is not a new problem. Once someone officially weights in over their max, they are given a chance to weigh in again in a month. You can tell who's getting weighed soon by who's in the base gym's sauna trying to sweat off the last couple of pounds!
if they bust their re-weigh-in, they are sent for a medical eval. If the doctor thinks they are at a healthy weight, then the max limit is increased for that member, and nothing else is done. If the doctor decides the person should be under the standard max, then the person is automatically enrolled in a weight management program which includes dietary counseling and mandatory PT/Exercise as a group every weekday morning before the duty day starts.
As long as they are making progress and losing a couple of pounds per month, they remain on active duty and on the WMP. Once they make weight, they are still on a WMP, but don't have to attend the mandatory PT. Weight is monitored weekly, and any relapses are addressed and corrected.
Weight is a difficult thing to manage for some, depending on their personal problems, lifestyle, and external influences.
i was over the max limit in HS, and when I became an ROTC scholarship finalist, I was riding a bike for hours everyday that the weather allowed. i rode all over the county and city near my house -- near being 10-15 miles.
I dropped 20 lbs in 2 months and even more when I started college by making smarter choices and being less sedentary. We had to run our 1-1/2 mile qualification test every semester, and I hate running. Took me 3 tries to make it around the track all 6 laps without puking. After that, i started running regularly just to be sure i could make my time.
The key appears to be motivation. Without the proper motivation, people will do whatever they feel like.