I have no doubt that Zach, like so many abusers before him, has also discouraged Heather in a hundred ways, large and small, from taking better care of herself or looking better. All the "Hagrid" "think I'm her daughter" stuff is devaluation intended to make her believe she couldn't possibly do better, and is in fact lucky for having a parasite as good-looking and kind as Zach.
If Heather ever tries to look conventionally prettier, even just with some nice clothes, hair that involved more styling or attention, or makeup, he probably mocks her for it. Probably calls her a "Karen," or asks her if she needs a pumpkin spice latte. Anything to double down on her fear of conformity. He probably positions her ugliness as genuineness, while simultaneously making sure she believes no one but him would tolerate the way she looks.