Insofar as vitamin D does play a role with regards to immunity(white blood cells have receptors on them), yes, levels do matter and certainly can help in addition to vaccination. As just a hormone however, it's not going to work miracles if something else can mechanistically cause damage, such as having untreated periodontitis or continuing to eat a high sugar diet(it might mitigate or delay the damaging effects of perio). Or in the case of obesity, it might help in certain aspects but not other things caused by being obese.
As far as obese people go, they have so much fat storage available that vitamin D levels in the blood are lower as it winds up in the fat cells and they have to consume more to maintain levels. Thus, supplementing vitamin D may help in the immediate timeframe, but treatment of weight is the necessary long-term solution. What is misunderstood, is that obesity is often a combination of multiple factors, which include hormones, mental health, and ignorance of what actually needs to be done to make it much easier to lose weight.
The obesity crisis(and the coinciding diabetes crisis) is a crisis of both profit and government-induced delusion(which ties into profit). The food industry lives...and thrives on sales. So does the exercise industry, certain medical professions like dentistry, etc. Where hormones come into play is foods that primarily stimulate the release of insulin, aka the simple digestible carbohydrate. These foods happen to be the most pleasing to eat or substantially enhance the palatability of foods eaten along with it, which includes meat and/or fat, sometimes deceptively so. Bread and rice, seemingly plain foods, actually have their own power in making the other foods more desirable. Furthermore, they trigger a physical cycle when the blood insulin levels drop, and then that triggers a hunger response a mere 2-3 hours later. Insulin also inhibits fat metabolism and promotes glucose metabolism.
Sweets and grains can also make one habitually eat more sweets and grains at the expense of other more nutrient-dense foods.
Despite the above being established knowledge, what is called "the carbohydrate" occupies an sacred, hallowed space as the omnibenevolent sacred macro; a holy foundation of healthy eating. Sugar is called sugar, even though it is a carbohydrate. So in the minds of many, it's as if sugar and other carbohydrates are completely different foods; such a thing manifested in the first food pyramid by the US, where sweets could be eaten sparingly but grains(and back then it was simple refined grains) could be eaten with impunity with 6-11 servings a day. And given the recent momentum of research against sugar, there is a begrudging concession at to cut down on "added sugars".
As far as mandates goes, the barring of unvaccinated from entering restaurants may have a pleiotropic effect as they cannot consume restaurant food in person. However, if takeout food replaces in-person dining, or a starch-heavy diet is eaten at home, then the person is setting himself up to fail in health over time even if COVID never reaches him.
As far as association goes, the lab coats, corporate suits, and the silver-tongued government officials sure milked choosing the less risky road based on association by essentially saying "don't take your chances" with regards to saturated fat and ultimately committed manslaughter against an enormous amount people by leading them to trans fat ridden margarine. Unlike disasters wrought by economists, there is no public outcry because this damage is "silent" and the perps can claim ignorance. Furthermore, the ones still clinging to the old paradigm are doing their darndest to prevent research to the contrary by simply not letting the funding get to the contrarians.
consultqd.clevelandclinic.org
pubmed.ncbi.nlm.nih.gov
www.kxan.com
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