Bride is literally the product of her parents' marriage, whether they like it not. So when seeking to understand what her character represents, and what a fair analysis of the plot might be, a good starting point might be to consider Bride as the aspect of her parents that they are ashamed of. Because they take pride in being light-skinned, their child represents the part of their selves they are most ashamed of.
The novel asks the reader to consider why these people should hate their blackness, and offers Bride as an explanation. Bride also starts to hate herself, because her parents reinforce the bigoted points of view that are available in their broader community. Since racism prevents people of color from being treated as equal human beings, the community has grown to associate lighter skin with more favorable treatment. Bride's blue-black skin is an obvious sign she will not thrive in this world.
The argument against racism is plainly obvious, but one could argue that the novel is really attempting to instill pride in the Black community so that growing children aren't made to adopt the shame that defines Bride's experience. Sweetness's name is an ironic reminder of this shame, because she is so ashamed of Bride that she literally refuses to let her own daughter call her "Mom," making her call her Sweetness instead, as if there is anything sweet about it.
