We're only finding this stuff now because the problem has grown to the point where researchers are specifically asking "why the heck are we so much fatter now?" They are finding multiple answers.
It turns out that real viruses can hack your body and change your persistent settings, just like software viruses can get into your computer and install a botnet rootkit. Some of those settings aren't even accessible to users. (I know if I had a slider bar to change my own body's preference for fat percentage, I'd drag it to 20% and tap the lock icon.)
Learning about this stuff, I now look at fictional plot devices like the super soldier procedure from "Captain America" in a new way. The machine demethylated all the DNA in Steve's body, and the serum injection targeted some specific genes to be re-regulated. Rather than chopping up the genes as CRISPR/Cas9 would do, an epigenetic regulator nondestructively tuned them, and set up positive feedback loops to keep them tuned to the "maximize Nazi-punching" profile. That's still far beyond our current abilities, but it makes it all seem more plausible.
Cowpox conferred immunity to smallpox--the similarity that led to the invention of vaccination in the first place.
It might be possible that some routine vaccination employs a virus that has always been considered completely harmless, with no visible symptoms beyond a little soreness and nasal sniffle, and that virus actually causes epigenetic changes that impact appetite and satiety, just like Ad-36, Ad-37, and Ad-5. There are about 50 known human adenoviruses, and less than 10 are believed to cause additional obesity. There are also viruses that are mainly pathogenic in other species, which cause no obvious symptoms whatsoever in humans--and in other species that are not the main host species--other than an increase in body fat. There are a lot of viruses out there. Only a small fraction have been studied extensively. Few would care to fund a test for antibodies to a virus that no one is afraid of, and that's what is needed to establish a correlation between exposure and obesity. The only reason adenoviruses were studied for this at all is because the avian virus that caused chickens to die fatter was denied an import license, and the researcher had to find something else that was already endemic.
Sometimes, a virus can be added as an adjuvant. It doesn't even have a direct impact on the targeted dangerous virus, it just makes the vaccine more effective by stirring up the immune system a little.
So it is entirely possible that vaccines that use live viruses that are traditionally considered harmless have never even tried to evaluate whether those viruses have impact on weight gain 10 to 20 years later. Those kids of anti-vaxxers that somehow survive to middle age might just end up with a lower average BMI than their vaccinated peers. It might be the only way we'd ever know. Usually, people who are not vaccinated live in a completely different culture, that would confound all the variables. An American anti-vaxxer living the same lifestyle (aside from the addled parents) as an immunized American would be a more apt comparison. The only other way to test would be to change the composition of the vaccine (an act that has an ethical impact) and wait a few decades to weigh people and caliper their back fat.