Than say fat white women, or even more fat East and South east Asian women? In a sense the question ignores the context of female racial beauty hierarchy. Black women are seen as at the bottom. Not so much for how we look, but because ideas of femininity clash with what black people are supposed to be, which are the opposite of feminine as a whole.
Morally lax, rascally and sly, as opposed to puritan, upright and honest, wild and savage, rather than demure and placid and so on.
White people are supposed to personify the more prosaic traits and that is joined with the idea of womanhood.
That is why the stereotype of black men is "hyper masculine", blackness doesn't undermine masculine ideals, but it does undermine their self expression. Black men have been skillful in many ways to overcome that the degree that they have, through artistic expression and so forth.
As black people are poorer overall, there's a class element in this. Working class white people also have a different relationship with fatness and women, similarly it could be seen as "easier" than for middle class white women in that sense.
But of course would be out of context, more than scaled back by the way working class people are seen as inherently degenerate because they've failed to attain a higher class status. There is no reason for anyone to be WC unless there is something wrong with them.
Though lower middle class people stretched by aspiration and needing to fit into another class band can also be quite fat
It's not that its okay to be a fat black woman, its that black society just hasn't reached the pitch of hysteria about thinness that other races have.
It's simplistic to state there aren't grave penalties for a fat woman who is black because it comes at a price that overrides any advantage conferred by a less mentally unbalanced level of vitriol towards fat women. It is seen as a shame, as a personal failing as my experience shows, I took being fat very hard indeed, even the idea of it didn't sit well with me.
Yet, I don't have some of the hang ups that white women seem to have about being judged on that score, I have others. Having to develop a more internalized sense of self worth and being more aware that people actually loathe you on sight makes the idea of undermining seem more costly and pointless and not really an available choice.