This post is based just on the books. I have not seen the movies. I'm assuming a certain familiarity with the books, but have included links to wikis where-ever necessary.
It doesn't need to be said that JK Rowling has exercised a lot of power over the imagination of millions of fiction lovers, young and old, in the last decade. I would not be surprised if the Harry Potter series turns out to be the longest lasting and most consequential work of literature from the turn of this century. And she has often used her wide audience to decry injustices. In “For Girls Only, Probably”, she states eloquently, “is 'fat' really the worst thing a human being can be? Is 'fat' worse than 'vindictive', 'jealous', 'shallow', 'vain', 'boring' or 'cruel'?”. This post on her website is not perfect – there is some troubling devaluation of thin bodies and ableism around eating disorders – but in places, it's a very well-articulated argument against the veneration of thinness.
In re-reading her Harry Potter series, I was initially discouraged by her explicit early associations between fat and evil and fat and lazy and fat and unhealthy. But as the series progressed and Rowling found her voice, I found an interesting evolution of her attitude towards fatness. Though there are very dim notes in her characterization of fat bodies (the Dursley family in particular), Rowling usually presents fatness as neutral and natural – some bodies are fat, some bodies are thin, and none are worth less for it.
In the early Harry Potter books, I was initially struck by the rampant sizism in her description of the Dursley family. Rowling echoes tired media tropes when she reduces prominent fat characters to one-dimensional comic relief, using many other harmful stereotypes in the process. Harry's cousin Dudley is dehumanizingly described as “the size of a young killer whale” and “a pig in a wig”, and his uncle Vernon is “beefy”. Petunia, too, is targeted because of her size: her thinness is as grotesque in characterization as Dudley's fatness. Their size is also explicitly connected to harmful stereotypes about fat people: Dudley is lazy and eats in an exaggeratedly unhealthy fashion, and he uses his size to menace people up through book five. Dumbledore, the most authoritative character in the series, even describes Dudley's appearance in book six as “abuse”.
However, these insults are softened considerably in the later books (the above quote from Dumbledore notwithstanding). After book five, Dudley's body is no longer a point of mockery, but a sign of his maturation and growth as a person – though he is still big, his size is connected to his physical ability and activity in boxing, rather than his laziness. This is tempered by Rowling's portrayals of Horace Slughorn and Hepzibah Smith. The size of both are painted in exagerrated terms, and in both fatness is connected with luxury. Neither depiction connects fatness with lack of health, which is something, I guess. But neither are particularly positive: both are slightly grotesque because of their fatness, and Smith's lack of beauty was noted several times. Aside from this, the later books treat people of size much better. I believe this is because of Rowling's growing awareness of the impact of her words; the social relevance of the series grew considerably in the later books, and I hope that Rowling reread these early characterizations and cringed and changed.
Though the early books in the series are more frequently plagued by sizism, there are some positive depictions of fatness early on. Most radical and normative of these (to me) was the presence of the Fat Lady as the guardian of the Gryffindor common room. The Fat Lady is a minor character most often used for texture comic relief, but she is still a major presence throughout the first six books. Like many peripheral characters, she is given a good deal of shading throughout the books; she is friendly, dependable, and sometimes a little bit irritable. Though fatness is her distinguishing characteristic, it is not a judgement on her value or attractiveness; much like the bloodiness of the Bloody Baron or the state of Nearly Headless Nick's neck – though I will note that it would have been nice if she'd gotten an actual name, like Sir Cadogen. She is fat, and she is funny to the reader. But what's funny are her quips in replies to students seeking entry – not her size. Most appealing to me is the use of fat as a neutral adjective in its application to her. She is fat, and that's how she's distinguished, and that's okay.
Another strong positive depiction of fatness throughout the series is Molly Weasley. Her plumpness is neutral to positive; she is described warmly, and her size is part of her appeal as a mother figure. Mrs. Weasley's constant busyness as a member of the Order of the Phoenix and a mother of seven are also a counter to the connection of fatness and laziness. The association between fatness and maternal qualities is not exactly trope-busting, but it's positive nonetheless – full-time motherhood and fatness are often devalued, so I was happy to see them embraced in this series. Mrs. Weasley is also an opportunity for Rowling to explore sizism; she is negatively described as “fat and ugly” by Draco Malfoy, and this is seen as a part of his distasteful and hateful character.
The Weasley family as a larger unit does a great deal to disassociate size from health and eating habits. Ron, who is described as slender, eats a huge amount of food, particularly sweets; he is always eating Chocolate Frogs and Cauldrons and reaching for yet another helping of treacle. This gluttony from a thin rather than a fat character is a helpful counter-example to the blatantly sizist descriptions of Dudley Dursley mentioned above. When Mrs. Weasley is described as “thinner”, it's not seen as a triumph of weight loss but instead a sign of her ill health. This characterization of thinness is repeated throughout the series; it's also applied to Tonks and Lupin, particularly in book six. Lupin's thinness throughout the series is a sign of his inability to gain employment because he is a werewolf. Tonks' size is a matter of illness – she is sick for love with Lupin. Women losing weight for unrequited love is a well-worn cliché. But both of these examples present thinness as not a matter of will or a matter of morals, and that contributes to Rowling's disassociation between thinness and health and worth in her later books.
“Fat” is not quite the right word for Hagrid, but he is certainly relevant to discussions of size in this series. The clearest description of him as “twice as tall and three times as wide as a normal man”, which suggests that he is fat as well as tall. Again, his size is seen as neutral and just a fact of who he is. Unlike Dudley, his size is not threatening – he is one of the sweetest characters in the series. Like Mrs. Weasley, he receives discrimination for his size: Professor Umbridge and others openly question his competence because of his size. Though the discrimination that he receives is more about his birth and not solely his girth, his oppression is relevant to sizism.
The magical intersection of fatness and part humanity also brings about my favorite writing of fatness in the series by far: Madame Maxine, headmistress of Beauxbatons. Maxine is, explicitly, both huge and beautiful. She is introduced alongside the most emphatically beautiful woman in the series, Fleur Delacour; in many writer's hands, this would be an opportunity to achieve comic relief through making fun of the fat lady. But Maxine's comparative body is presented as complementary to Fleur rather than contrasting. Maxine's attractiveness and polished presentation are consistently emphasized alongside her size (she is described as “handsome” and “well-dressed” repeatedly). Her comparative size is not a point of mockery, but a fact of her existence.
Though there are problems with Rowling's depiction of both ends of the size spectrum, the Harry Potter series is generally successful in communicating that there are not defined relationships between weight and health, or weight and beauty. In general, Rowling treats both fatness and thinness as neutral adjectives that imply different things for different kinds of bodies. This is not a radical act, but for a writer with the audience of Rowling, it is a positive and a productive one.