Choji Akimichi from Naruto. Oddly enough, it appears to actually be true, since by the time of the timeskip he's certainly not svelte, but looks more like a linebacker, suggesting that he grew into his body.
Axis Powers Hetalia — A fan asked Word of God if Russia was fat, and they received an in-character answer from Russia saying exactly this. He was later shown in a shirt that said "Big Boned" and appeared to be struggling to fit it. The few instances we've seen him without his coats, he appears to be rather muscular.
Fist of the Blue Sky: Zhang Lie-Shan, boss of the Hong Hua-Hui Triads a man gifted with "exceptional stature"... as in "literally the height of a three stories tall building" exceptional stature. However, he is incredibly sensitive about being out of the ordinary, and gets very unhappy about being called "too big"... as in "smother his tree sized cigar into your face and drown you with his car-sized shot glass of whisky" unhappy.
In the Scare Tactics comic, Grossout's mother kept insisting that he was just "big for his age".
Obelix from the Astérix comics. ("I'm not fat. I'm just... well wrapped.") Calling him fat is almost a Berserk Button with him.
A joke in the screenshots and fanfics on Raquaza Master's Pokétown Pokémon board featured a character calling Ash fat, and he would reply that he was big-boned. It's even funnier when you notice that he isn't fat at all.
Inverted in Evas XLR. Shinji Ikari calls his cousin Coop big-boned. Coop doesn't like it.
Jennings: My size is due to a glandular condition, Mr. Keogh.
In Harry Potter, the Dursleys make excuse after excuse for their son Dudley, saying that he still has baby fat/is big-boned/is a growing boy right up until his school sends a letter saying they no longer have uniforms that fit him.
In the same book, Hagrid, who is described as being twice as tall as a normal man and five times as broad, admits to being a half-giant and asks the similarly-built Madame Maxime about her own ancestry. Madame Maxime is very offended, and claims to just have big bones. Harry and Ron don't buy it for a second:
Harry: I don't know what Madame Maxime thinks she's playing at. "Big bones", the only thing with bigger bones than her is a dinosaur.
In Supergran by Forrest Wilson, one of Supergran's sidekicks is on the large side, but tells anybody who brings it up that "It's not fat, it's muscle". The disclaimer is so firmly ingrained that when, at the end of the book, somebody remarks on his muscular physique, his mouth says "It's not muscle, it's fat" before his brain catches up.
In Robert Kimmel Smith's Jelly Belly, Nathaniel's grandmother insists that her darling grandson isn't overweight; he's just big-boned like her. Even after Nathaniel himself tries to get her to acknowledge that he really does need to lose weight and that she could help by not cooking so much food for him.
In Stephen King's It, the back story of Ben's weight loss as an adult includes his confrontation with his mother. Keeping her son well-fed was a comfort for her, so she made the excuse that he just had big bones.
Molly's Mom: You're not fat, dear, you're just big boned.
Molly: Bones don't jiggle, ma.
Married... with Children: Al Bundy's mother-in-law isn't fat. She's "retaining water". Al replied the Hoover Dam was retaining water.
Garfield does it sometimes, a few with the trope name (the page image is the response of his sarcastic bathroom scale).
In January 29th, 1979, Garfield literally claimed to be big boned. Jon called Garfield "disgustingly, slovenly, sloppy fat" and Garfield said Jon obviously had "disgustingly, slovenly, sloppy fat" confused with "big boned".
Bart tries the "I'm big boned" excuse at fat camp in "The Heartbroke Kid". He gets told there is no such thing and whipped.
Manfred in Ice Age: "I'm not fat. It's all this hair. It makes me look poofy."
Doug had a crisis when he had gained weight and worked out hard to get back to his normal weight, but realized he was always a little chubby. As he talked with some chunky friends, they each gave some alternate terminology like "big boned" and "stout". When Doug asked what he was, they said, "Husky?"
In Gummi Bears, Tummi uses this excuse that he has "big bones," to which Gruffi snaps, "Yeah, and they're getting bigger."
Donna: I suppose you brought your hobbit friend too.
Colt: That's offensive. I'm small boned. Except for one. This chick gets it.
There was an episode of Johnny Test where Johnny made fun of a video game vendor for being fat. He claimed it was a "glandular problem". The episode was based off of the concept of karma, so when Johnny ate an experimental candy bar, it messed with his hormones and made him fat as well. In other words, he now had a glandular problem.
In Futurama, Hermes sees himself through an X-ray. Not only is he not big-boned, but if it wasn't for all that fat, his skeleton is so small that he would effectively be a dwarf.
When Amy's parents call Kif scrawny, Amy says he's just "small-boned". Kif notes that he actually has no bones.
Fred Flintstone isn't fat. It's all muscle. He then dared Betty to sock his belly to show it. She answered the dare. Fred felt pain but wouldn't scream until he was sure he was out of her hearing range.
Tiny Toon Adventures: Sweetie was once adopted by an eagle she called fat. His reply was the same as Fred's. To his dismay, she enlarged her hand.
Inverted in real life. Having a large bone structure makes you look less fat than you are, not more. A person with a very large frame and 30% body fat will appear slimmer than a person with a very small frame and 30% body fat.
Mass gain from fat is impossible without overeating relative to your activity level, because it would violate the laws of physics (matter-energy can neither be created nor destroyed, only transformed; thus, the only possible source of fat in your body is from the foods you consume). However...
Certain medical disorders and medications can cause weight gain in the form of water retention, where excessive amounts of water are stored in the body, despite not consuming more calories than is necessary for the body to function. This usually goes away once the underlying medical disorder is treated, but in some cases requires medical intervention.
Hypothyroidism and related thyroid problems are often cited as a cause of weight gain. However, in reality, only about 5-10 pounds of weight gain from hypothyroidism is typically caused by the hypothyroidism directly in the form of water retention; fat gain is indeed due to overeating relative to energy use. Many people with hypothyroidism feel constantly fatigued, and as a result become more sedentary, which reduces how many calories they burn, so even if they eat a seemingly normal amount of food, they may still be "overeating" if they aren't burning many calories.
Congestive heart failure can cause considerable water retention.
Pregnant women frequently retain water, especially in the feet and legs.
Some medications and medical disorders also affect appetite by making people "feel hungry" more often. This does not cause weight gain in and of itself, but as a result of increased feelings of hunger, many people suffering from increased appetite end up overeating because they don't monitor their food intake.
Because of its culture, many Pacific Island natives have bigger bodies. This is because, in their culture, being larger is still seen as a sign of wealth. Because of the drive to be a bigger race, many Islanders have the same body type as described above.
Polynesians have on average the most muscled bodies of all races on Earth (with the unfortunate effect that their endomorphic physiques gain fat even quicker than other people). In Peter Jackson's Lord of the Rings films, most Orcs (who were supposed to be muscled and have high physical strength) have been played by Maori actors for this reason.
Mexican actor Edgar Vivar claims he is not obese and says he does has fat but "resting muscles", or at least so he did in an interview.