willowsevern has already put together lists of canon references to Gregory, and so I'm just linking to them.
Harry Potter and the Philosopher's Stone
Harry Potter and the Chamber of Secrets
Harry Potter and the Prisoner of Azkaban
Harry Potter and the Goblet of Fire
Harry Potter and the Order of the Phoenix
According to the screenshot of JKR's notebook [which is currently not accessible online, but I have a copy], Gregory is a pure-blood wizard. His father is a Death Eater, who according to this page is at large, but there aren't any direct canon references to this.
Gregory is thickset, mean-looking, large, thuggish, wide and muscle-y. He has long, gorilla-ish arms, a broad back, large feet (four sizes larger than Harry's), thick fingers with broad nails, and bulging knuckles. His mouth is so large, he could stuff a plump chocolate cake into it whole when he was 12. His eyes are small, dull and deepset. He does not need glasses to see well. He has a low, raspy voice. He was a lot bigger than Harry and Ron when they were eleven. He was at least a foot taller than Harry when they were twelve. He grew at least a foot during the summer before fourth year. He's shorter than Vincent Crabbe.
He and Vincent get into a fistfight with Neville during the Quidditch game in PS, which resulted in Neville being out cold long after the game.
In CoS, his hairstyle included a fringe down to his eyebrows. In PoA he has short bristly hair with no mention of a fringe. His hair resembles bristles to the touch. He wore moss-green robes to the Yule Ball and had not managed to find a partner. He wears boatlike shoes with laces in them.
He follows Draco around and always does whatever Draco does, seeming to exist to do Draco's bidding and look to him for instructions. Hermione says that Gregory (along with Vincent) are Draco's best friends, and that Draco will tell them anything. He kept a lookout while Draco talked to Beetle!Rita in GoF.
According to Harry, Gregory is almost as stupid as he is mean. So he's mean and stupid (like all Slytherins, of course *snerk*). He passes in all his classes nonetheless. It is apparently bizarre to see him thinking. He looks bewildered when a teacher asks him a question. Even Draco insults him for being slow on the uptake. A potion he made during fifth year was so bad that it shattered a flagon it was poured into and set his robes on fire. He hates writing. Does not look bright enough to tell one end of a broom from the other, according to Angelina Johnson.
According to Hermione, he is fond of food to the point of being greedy. He seems to particularly like trifle. Finding unattended chocolate makes him look triumphant (I'm WTFing right along with you, trust me...).
Polyjuice potion with his hair in it turns the khaki colour of a bogey.
Draco was standing on his shoulders during the fake Dementor stint in PoA. He received detention as punishment for participating (50 points were taken from Slytherin, but that seemed to be for all four of the pranksters). He was sent to try and sabotage Harry (by tripping him up and such) before the Slytherin versus Gryffindor game in PoA.
He was bitten by Scabbers (on the knuckle) aboard the Hogwarts Express during his first trip to school, which caused him to howl in pain and swing around to try and get the rat off. Harry deliberately chose Gregory's cauldron to lob one of his Fred's Filibuster fireworks at when the Trio needed a distraction in Potions during CoS. After receiving a faceful of Swelling Solution, his eyes were as large as dinner plates. Gregory was hit in the face by Harry's Furnunculus curse that was meant for Malfoy. Boils sprang up on his nose that made him resemble an illustration in a book on poisonous fungi. These were bad enough to require medical attention. He's hexed into something resembling a gigantic slug squeezed into Hogwarts uniform by six DA members. According to Ron, looking like a slug improves upon Gregory's appearance greatly.
During a Care of Magical Creatures lesson, he was one of the first to flee to Hagrid's cabin when the Blast-Ended Skrewts didn't appreciate being forced to hibernate.
He tried to steal leprechaun gold during another Care of Magical Creatures lesson.
He looked more arrogant and menacing than ever when he showed up in Harry's compartment on the train ride home in GoF.
Fred Weasley stepped on his unconscious body (covered in hex marks), which was then kicked, rolled, and pushed into the train corridor. Harry stepped right over him as he disembarked.
Starting from 5th year, he's a Beater for the Slytherin Quidditch team. During his very first game, he hits Katie Bell with a Bludger.
Did his Charms O.W.L. at the same time as Anthony Goldstein, Hermione Granger, and Daphne Greengrass.
He is uncomfortable at hearing Voldemort's name spoken by Harry.
He took McGonagall's cloak up to her office at the end of fifth year.
He finds it amusing when people (Draco, Snape) make fun of Harry, Neville, and Gryffindors in general. It is not stated explicitly, but he appears to be a member of Umbridge's Inquisitorial Squad (he would have to be, given the fact that he does everything Draco does or tells him to).
Draco more than likely knows him from before -- that is, they had to have met before they boarded the train to Hogwarts. Be it social status or Draco's ability to play people, Gregory defers to him and acts as his bodyguard; no eleven-year-old boy can command instant loyalty. So it's unlikely that Draco met Gregory for the first time on the train. There is an apparent expectation for him (as well as Vincent) to save Draco's neck if need be, so I wonder if perhaps there is a similar parallel between Lucius and the senior Goyle (and Crabbe).
Gregory possibly doesn't take physical pain very well. Most people say "ouch" or something along those lines, even kids -- Gregory let out a horrible yell and then howled when Scabbers bit him. His swinging around to try and get the rat off appears to be more cruel comic relief rather than an attempt to be realistic on the author's part. If a rat attaches itself to my hand, I might shake my hand frantically to try and get it off, or I might grab the rat with the other hand and pull. I wouldn't swing the thing around, and I'm not a fan of physical pain, either. He might have a scar on his knuckle from when Scabbers bit him.
During CoS, Gregory had ostensibly asked Draco repeatedly about the identity of Slytherin's Heir. I say this because Draco says "How many times do I have to tell you?" when Goyle!Harry asks him that again.
He could possibly be afraid of ghosts (he looked scared when Harry was lobbing dirt at them in PoA).
It's possible that his family is not rich; he tried to steal leprechaun gold and looked sulky when caught -- neither Vincent nor Draco did this.
He's certainly not very popular with the Slytherin girls (or any girls, for that matter) -- unless he hasn't bothered asking any girls to the Yule Ball, it's possible that he was snubbed even by the girls in years below fourth. The Yule Ball was an occasion people were dying to go to, and for a girl to refuse to go with Goyle, there'd have to be some weighty reasons. These may include but not be limited to his being ugly, brutish, or even not rich enough.
The arrogant and menacing looks, and his behaviour during the train ride to London in GoF, suggests that he is pleased that the Dark Lord has returned. Considering that Draco spent some time whispering to him and Vincent during the Leaving Feast, this may or may not have involved some convincing. (Goyle, think for himself? Perish the thought. He's just a nasty smelly Slytherin. *snerk*)
He appears to be even worse at Potions than Harry. Harry seems to think Goyle is even more stupid than Crabbe. Judging from the pretty picture next to "Troll" in Harry's copy of Fantastic Beasts and Where to Find Them, as well as from dropped comments by both Harry and Ron, it's pretty safe to say that for some reason our Gryffindor main characters dislike Gregory moreso than they dislike Vincent.
Despite Harry and Angelina's thoughts to the contrary, he seems all right with a Beater's bat -- considering that he hits Katie during his very first game, whereas Ron can barely save a goal during said game.
He does not go so far as to openly question teachers' authority (he takes McGonagall's cloak up to her office wordlessly, despite all the Dark Lord bravado). So perhaps he's not as stupid as he looks (I'm not even going to start on the fact that he passes in all his classes year after year...).
By all appearances, Gregory is unquestioningly loyal to Draco Malfoy. The fact that he's so prone to laughter always makes me think that he's generally a good-natured boy who likes a good laugh. He just happens to have committed the unforgivable crime of being in Slytherin and friends with Draco.
He may actually be mute (I'm being deliberately tongue-in-cheek here, but honestly, a character with over 100 mentions and without a single word spoken?).
In case it wasn't obvious from the detailed account of his injuries above, Gregory actually suffers far more abuse from Harry and his friends than Harry ever does from him, if we go on nothing but what is specifically said in canon. Gregory does a bit of threatening muscle-flexing (not nearly as much as sycophantic laughing, however), it's repeatedly said that he's big and a thug, and he's once sent to trip Harry up... but does he ever actually hurt Harry? Not once. Draw your own conclusions.
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