Vegan

Assuming that an overweight person must eat meat is a logical fallacy.

I wasn't assuming that.

You're hyper focusing on one detail and missing the forest for the trees.

Premise 1: The vast majority of people eat meat

Premise 2: The majority of people are overweight

Conclusion: A very large portion of the population can stand to eat less meat.

Add in that some meat (beef) is a lot more caloric than anything green, and the likelihood of an overweight person being a vegan is quite small (which doesn't mean there aren't cases of it), and so the number of people who can stand to eat less meat also grows higher.

I'm not trying to shame people for being overweight, I struggled with it for a long time myself, I'm simply pointing out that the majority of people can definitely afford - both money and health wise - to eat less meat than they do.