Indeed, the National Association to Aid Fat Americans (NAAFA), now the National Association to Advance Fat Acceptance, was founded in 1969. In 1973, an activist group "Fat Underground" had a manifesto that included "We see our struggle as allied with the struggles of other oppressed groups against classism, racism, sexism, ageism, capitalism, imperialism, and the like." Since at least the 80s, fat people have used the phrasings of "coming out as fat" / "come out of the closet" to mean their acceptance of their bodies/not finding fatness offensive/no longer stressing about dieting.

What's interesting is the question of agency getting tied up with fatness in the first place. There have been times even not that long ago that being fat was considered a sign of success. There were even these "Fat Men's Clubs" (https://en.wikipedia.org/wiki/Fat_men%27s_club) of rich and fat businessmen celebrating their weight and eating a lot. But then fatness became bad, marking a lack of agency, and acquired other negative aspects like being greedy (contra magnanimous) and stupid and having 0 sex appeal (contra, say, the Venus of Willendorf, though you don't really need to go back that far), and being unhealthy, and being an overall burden to society whether it comes to airplane seats or healthcare costs.

Since dieting/keeping slim in the face of our modern abundance is now considered a mark of successful exercise of agency, fat acceptance types have to somehow decouple their eating behavior from their weight, if they want to maintain some semblance of agency here. (Despite the way our culture seems to be moving I still think most people want to maintain an idea of agency, even if that's in going against what it means to be agent-y.) So sure the 'fatness' is something that just happens to them, like being tall or short, it's not even unlucky really, and it's pretty much impossible to change in the long term anyway (with even some science backing up the failures of long-term weight loss after dieting). However they can twist it, the goal is to be free from the moral failing/agency failing concern that they're not acting in responsible/good ways. They can still be considered good in other ways.

And now that they're no longer preoccupied with their "exercising agency" failings from fruitless dieting and what have you, they begin to exercise more agency! Check out this cover letter from 1981 by Wilma Kuns on how she was able to start living her life once she accepted her fat: https://naafa.org/s/Nov-Dec_1981.pdf I think it's pretty typical, even today, and sure is reminiscent of other groups' "coming out" expressions of exuberance. Instances of exercising agency can be as simple as throwing out a scale, or a sense of a new-found ability to actually make choices and decisions (the foundation of agency) for things like clothing, sex (either feeling able to pursue it at all without feeling disgusted in themselves/partner, or being able to say 'no' and not just take what they can get), or doing activities or working jobs they wanted to do but were previously afraid of suffering social ridicule for. Having a bit of self-confidence feels like an agency booster, so of course removing this constant "you're fat and unworthy of life/fair treatment/love/health/..." mentality helps, regardless of whether it's rationally backed or not.

But it also gives a sense of agency in another way: exercising resistance, namely to society's (or some segment of society's) ideas of what it means to be healthy and beautiful. There's a lot of this form of agency these days. It's rather amusing that such acts of agency still reinforce the overall societal demand for agency, for distinguishing yourself as an individual making choices and pursuing what you think of as your idea of success.