Simply put, this character is outright attracted to fat people on an aesthetic level. Often treated as strictly as fetishists with inclinations toward feederism, if not outright as an Acceptable Target. In Real Life, some prefer the term "Fat Admirer."
Both labels are often applied to anyone who dates a heavy person but isn't overweight themselves, regardless of any other qualities they like in the person or if they simply find that person attractive with no particular fetish.
In a way, this is Truth in Television, as many ancient and modern cultures prefer hefty, moderately-overweight women to skinny ones. The pop-culture obsession with thin women is actually relatively new.
Related to Big Beautiful Woman, Big Beautiful Man and Fat and Proud.
In one of the Filler episodes of Naruto, there's a princess who hires Ino to pose as her during a meeting with her fiance until the princess loses weight. It turns out, however, that the prince likes his women pudgy (he's a big guy himself).
Ranma ½: This trope is referenced and combined with the You Are Fat trope for hilarity when Ranma's mirror clone tells Akane that Ranma likes her.
A one-shot character from Ai Kora was Gokou Ooba, a wealthy teen with a thing for fat girls who'd had a crush on Ayame's fattened-up version from an earlier chapter.
Katou Hayabusa is well-known for all of his mangas featuring a plump lady and/or a lover of such. This seems to be the whole point of Sea Side Bound. He's done mostly original, but he has done a few fan-comics, like Zero no Tsukaima and Kannagi.
Tagami, the male lead from the shoujo manga Pochimani is a self professed "chubby maniac" who loves cuddling his plump little girlfriend Tsugumi.
In Kare Kano, a supporting character bought and fed her skinny boyfriend large amounts of food, because she really wanted him to be fat again like he was when they were kids.
Deadpool is one and even goes on a date with Great Lakes Avengers' Big Bertha. He is so blatant about it that she tells him she feels as objectified as when she's in super-model mode, and wishes that people could look beyond her physical appearance and love her for her personality. Deadpool then takes his mask off to take her up on the offer... then comes her Vomit Discretion Shot.
Jimbo from Rose Is Rose prefers Rose if she were fat, so much that he often looks through wide reflections of her to fantasize about it.
Lex Luthor himself may be one. He's shown a romantic interest in the rather large Amanda Waller, and even passionately kissed her in Public Enemies. This may have less to do with her looks than the fact that she's one of the few non-superpowered women who can give the Justice League a run for their money, though.
Andy Garcia's lead in City Island has plenty of family issues: in his teen son's case, it's his love of Big Beautiful Women, including asking a fat girl at school to skip class with him so that he can feed her donuts, and a voyeuristic crush on their zaftig next-door neighbor. A foray in the dark corners of the internet leads him to stumble on a feedee webcam belonging to "Botero" — which is actually his neighbor's screen name. Hilarity Ensues. (When she discovers this, "Botero" does not kindle any romance with the boy, but rather plays Cyrano between him and the fat girl at school.) This subplot culminates with him on a couch, squished against the two objects of his affection while they munch on cheese puffs and watch TV.
"You're a classic feeder, Vinnie. You gain pleasure from giving pleasure."
The titular character in Shallow Hal becomes one through hypnosis. Once the love goggles have been lifted, Hal realizes the object of his affection is beautiful. Also, twice his size.
The Prime Minister (Hugh Grant) character in Love Actually. He flips for Natalie, a bottom-heavy member of his junior staff — but gets a bit defensive when people call her chubby. Which is often.
Aide: I'd say that's an ample ass, sir.
Stephen in Django Unchained, a strict taskmaster to the other slaves under his watch... except for Cora, the portly housemaid.
Miles in Summer Catch.
"Excuse me, I am tired of living a lie. I need it to be known that I like a big girl. In fact, a large, zaftig, voluptuous, full-figured, big-boned, massive-assive honey, that is what gets me going. I like fat women and they like me... big girls need love too, baby!"
The unfeasibly influential and rich media tycoon, Sean Cooley of Fat Slags. Then, after a hit to the head makes him forget that he keeps it secret, he is able to convince literally everybody in the United Kingdom that fat women are the epitome of fashion and sex appeal.
Moto Moto in Madagascar: Escape 2 Africa. He likes 'em big, he likes 'em chunky. Justified, as he's a hippopotamus.
In Role Models Wheeler tries to console Danny after his girlfriend moves out of their house.
''If she doesn't come back I'd go for that friend of hers in the sweater. I know she's a few pounds overweight but in my experience it's the bigger ones that do way more stuff."
Adrian from Pain and Gain, who goes after the fat nurse treating his erectile dysfunction.
One of the ladies from Waiting to Exhale, Gloria, finds herself single when her husband comes out as gay. Luckily, Gloria's new neighbor is a fellow divorcée — to a woman as large as she.
Professor Peach of The Italian Job 1969 is very very interested in big women. In fact, he agrees to do the job after one guy says Italian women are huge.
Roald Dahl's short story, "Madame Rosette" includes a conversation between a group of RAF fighter pilots and native Egyptians at a bar. They compare their tastes in women, finding that the Egyptians prefer them fat, whereas the English like them thin.
In Behold the Man, a time traveler lands in AD 28 to meet Christ, unaware that his arrival will lead everyone to believe he is the messiah. In flashbacks to the present, the protagonist has a tryst with an overweight girl at bible camp, mirrored in a strange scene with Mary of Nazareth (who is also quite hefty). His professor, whose theories made the time machine possible, also confides a certain affinity for large black women.
"Fat Fred," an "angel" from John Varley's Wizard. By the standards of a race that has next to no body fat and sees humans as rather pudgy, anyway.
Ray Bradbury's "The Illustrated Woman" features a man named Willy Fleet who when he first encountered his plus-sized wife rhapsodized that "Michaelangelo would have loved you. Titian would have loved you. Da Vinci would have loved you. They knew what they were doing in those days. Size. Size is everything."
In the Discworld series, the Senior Wrangler of Unseen University is implied to be one. In Hogfather he tries to court the plump and somewhat frumpy Cheerful Fairy, and in The Last Continent he's frequently distracted by thoughts of Mrs. Whitlow, the University's fat, middle-aged head housekeeper.
Kurik from The Elenium has a rather plump wife, to whom he is Happily Married. Another character even mentions that Kurik likes plump women. He oddly subverts this when he is revealed to have had an affair -and a child- with a woman significantly skinnier than his wife.
In Just Shoot Me! S04-E13 Dial 'N' For Murder, Maya is happy that she has started dating a man who dislikes the waif-thin look that her father's fashion magazine promotes. Unfortunately, she discovers that while she agrees with him, she doesn't want to let him fatten her up.
In Bones S5-E08 The Foot In The Foreclosure, the Victim of the Week was a former chubby girl who had been a regular at a Chubby Chaser hookup night-club. After she lost the weight, she went back as a chaser.
Bones & Booth take Booth's grandfather when they go to ask around at the club. When Booth asks Bones for a polite way of saying "fat", his grandfather tells him that there's nothing wrong with liking fat women, and that his wife (Booth's grandmother) had "a little jam in her jelly". As soon as he gets to the club, he starts eying up the BBWs on the dance-floor. When Bones & Booth are ready to go, they realise that he's already on the dance-floor grinding between the women he was eying up before, so they stick around for a while.
Cheers: A hot woman goes after Norm, to the befuddlement of the others at the bar (especially Sam). Paul (one of the minor characters who had an occasional Day in the Limelight, and who is also a chunky guy) identifies her as a "chubby-chaser."
In Todd and the Book of Pure Evil S01-E05 Monster Fat, Jimmy the Janitor mentions having slept with hot chicks, skinny chicks and even chicks with dicks. But the best sex of all is with fat chicks. Notably, the episode where he imparts this insight to the main character feature a Monster of the Week turning all the female students obese.
"When I want to grease my piece, I go obese."
In fact, one of the plot points of the episode is using a water pistol full of the instant obesity liquid to threaten the girl who accidentally made the fat monster. At the end of the episode, we see the Janitor on a date with an extremely attractive woman. When she leaves to visit the bathroom, he immediately produces another water pistol and squeezes it into her drink.
On House, S01-E16 Heavy, a patient's husband admits that he loves it when his wife puts on a few more pounds, especially when it means she's pregnant. For that matter, he seems to be even more turned on by a preggo wife on the whole. The patient likes her curvier body and downright becomes angry when the doctors told her that she needed to do a surgery that would cause her to lose weight. We later learn that she's been fooling around with other men who evidently were attracted to her size. House suggests that she switch to a website for surgical scar fetishists instead. Check and mate.
Hal of Malcolm in the Middle goes off the deep end when a pregnant Lois grows a few sizes. He spends a whole episode injecting maple syrup and chocolate sauce into her tea and, when she buys celery, fries it in bacon grease.
Noah's Arc: Alex (a self described Big Beautiful Man) hints that Trey may be this, but since Alex is the only guy we see that Trey has an interest in, its difficult to assess.
There is an episode of Yeralash where a boy brings a picture of two girls to a sorcerer and asks him to cast a love spell on "the pretty one". Next day, it turns out the sorcerer is a Chubby Chaser but the boy is not...
A Running Gag in the Grand Theft Auto series. Thor, modern-day viking and motivational speaker extraordinaire, mentions his preference for large lasses on Vice City's K-Chat radio. "A man needs something to grab onto!"
Same goes for Forth Right MC on San Andreas's Playback FM. "I want somethin' I can bounce up and down on!"
One of the player character's optional love interests in San Andreas is a female chubby chaser. Like all of the other women Carl romances, this is a way of getting more mileage out of the character customization. You can only date the gearhead Latina chick if CJ's fat meter is 50% or higher.
One sidequest in Yakuza 4 is, basically, a hunt for a Chubby Chaser. Akiyama's chubby-yet-cute secretary has suddenly gotten all depressed, and claims that no man would be interested in her (not that she's really outright fat - by American standards, anyway), prompting Akiyama to try and prove her wrong by tracking down a man who likes 'em chubby. After some false starts, he finds one - working as a 'recruiter' for a Hostess Club, though not for long since his boss is fed up with him always bringing back the BBW's instead of the lithe beauties that such clubs generally deal in. In the end, even though you convince this fellow to come back to your office, and introduce him to Hana-chan, it fails to noticeably improve her mood... since the reason for her depression is that she's in love with Akiyama, who—aside from being a hopeless playboy—has a decided preference for the traditional, slim body type.
In one quest in The Elder Scrolls III: Morrowind, the player must find a prospective wife for a dark elf noble, and according to him, she should be "pretty and plump, with big hips."
In Fable II, some of the NPCs in the Knothole Island DLC are "fat-loving", and will find your PC to be more attractive if they're overweight, rather than less attractive.
Being a Dating Sim series themed around courting heavyset girls, this is the entire point of Debu Plus. Case in point, New Debu Plus' male lead, Ruiga, is only attracted by that type of girl and decides to pick one of the three Kominezaki sisters.
World of Warcraft: The Pandaren, a China-inspired race of anthropomorphic pandas, consider chubbiness to be a highly desirable trait, both for males and females.
Pam from Archer is targeted by a rich German Chubby Chaser in one episode, much to Malory's disgust, as she was trying to seduce the man for her own agenda. They eventually get drunk and have a threesome anyway.
In Animaniacs, Dr. Scratchnsniff is almost always seen falling in love in a voluptuous lady.
In the Popeye short "Weight for Me" Olive comfort eats while Popeye and Brutus are away at sea and when they come back she's obese. While Popeye tries to help her lose weight, Brutus tries to get her to keep it on.