Why does Sykes dislike skinny women like Delia? Why does he like fat women like Bertha?

Sykes may associate being fat with youth and being agreeable. It's something that he's always been attracted to whether it's that association or just a mental preference.
Delia, his wife, works hard. She's a thin woman who looks like a hard-working, put-upon wife. When they fight, Sykes says, "Ah'm so tired of you Ah don't know whut to do. Gawd! how Ah hates skinny wimmen!" He's been mean, cruel, and useless but still blames her for his issues. He brings up that she's skinny either because her defiance reminds him of her light weight or because he's bitter that he isn't married to a fat woman.
Zora Neale Hurston makes it clear that Sykes has always liked fat women. One of the men discussing Sykes and Delia says, "Aw, she's fat, thass how come. He's allus been crazy 'bout fat women," put in Merchant. "He'd a' been tied up wid one long time ago if he could a' found one tuh have him." Delia at one point thinks that she used to be young and soft—which might mean she had more weight—but now, after years of hard work and an abusive marriage, she has "knotty, muscled limbs."
Bertha, the woman Sykes is sleeping with, is a fat woman. He may prefer her simply because he likes the look of fat women or he may prefer her because she's agreeable and doesn't have to work in the way his wife does. Hurston never says directly whether it's a preference for the look of thin versus fat or whether it's a preference for the lifestyle that comes with the body type.

Sykes most probably dislikes skinny women, such as Delia, because their shape suggests overwork. And to a perennially lazy good-for-nothing like Sykes, that's an uncomfortable reminder of his own invincible sloth. As an old-fashioned (i.e., sexist) man, he also doesn't like the idea of his wife going out to work for a living.
As for Bertha, she may be described—somewhat ungallantly—as looking like a hunk of liver with hair on it, but her womanly shape is so much more to Sykes's liking. Her ample size suggests a homely woman, a woman who will devote herself to the man in her life without question. For an abusive "alpha male" like Sykes, this is just the kind of woman he wants in his life, even if by common consensus, she's quite ugly. He wants a woman who will be at his beck and call 24/7, who will remain at home all day and not even think about going out to work.