It's a typical Narcissist thing. Narcs generally don't think about others' desires, unless it's somebody they are actively trying to impress because that person has higher status, or else is in a position to give them something they want.
If you're somebody the Narcissist takes for granted, then whatever the Narc wants, or is willing to provide for you, is wonderful. Therefore, you should want it too, and be grateful to them for offering or providing it. If you don't want it, there's something wrong with you; the fault is entirely yours. You're ungrateful; or have shitty taste; or have some psychological issue; or are just playing games and trying to be difficult in order to annoy them.
Narcs can't deal with people who don't validate them, even over something so trivial as the size of a piece of cake. So a thin woman asking for a smaller piece of cake can't simply want a small piece of cake because that's all she wants; her choice is an attack on Virgie. So Virgie turns the simple desire for a small piece of cake into something pathological--a sign of internalized fatphobia, of cruel self-denial, of shame concerning one's body, and of an inability to fully experience pleasure.
If Virgie was as in love with her own fatness as she proclaims, she wouldn't make anybody else's food choices an issue. She'd gladly cut the smaller pieces of cake and not even think about it. Maybe she'd laugh and say, "Yay! More cake for me!" But being shitty about it reveals just how envious she is of thin women, and how bitter she is at not being one of them, and how ashamed she is of her own gluttony.