"If he wants ter go, a great Muggle like you won't stop him," growled Hagrid. "Stop Lily an' James Potter's son goin' ter Hogwarts! Yer mad. His name's been down ever since he was born." (4.130)
As far as we can tell, the question of who pays Harry's tuition is not fully addressed in this scene. Instead, it's quickly overshadowed by the idea that Harry's lineage demands he go to Hogwarts. In a way, the school itself is loyal to the children of its alumni, reserving places for them as soon as they come into existence.
Harry, who hadn't had any breakfast, leapt to his feet, but Ron's ears went pink again and he muttered that he'd brought sandwiches. Harry went out into the corridor. (6.163)
Although Ron is embarrassed by his family's poverty – they just don't have as much money as other old wizarding families – he's determined not to show it. Although his "ears [g]o pink" and he clearly feels unhappy about not being able to buy any snacks on the train, he defends his family and his situation by telling Harry that he's already got "sandwiches."
"Gryffindor," said Ron. Gloom seemed to be settling on him again. "Mom and Dad were in it, too. I don't know what they'll say if I'm not. I don't suppose Ravenclaw would be too bad, but imagine if they put me in Slytherin." (6.225)
Family loyalty works in reverse too when you're a Hogwarts kid – children of alumni feel an obligation to end up in the same house as their parents. The idea of not being in Gryffindor like his parents fills Ron with "gloom." He can't even "imagine" what they would do if he wasn't: "I don't know what they'll say if I'm not." While Ron seems unable to even countenance the idea of being a Slytherin, notice that he doesn't even mention Hufflepuff at all.
"I think I can tell who the wrong sort are for myself, thanks," he said coolly.
Draco Malfoy didn't go red, but a pink tinge appeared in his pale cheeks.
"I'd be careful if I were you, Potter," he said slowly. "Unless you're a bit politer you'll go the same way as your parents. They didn't know what was good for them, either. You hang around with riffraff like the Weasleys and that Hagrid, and it'll rub off on you." (6.246-248)
Being the right sort or the "wrong sort," worrying about being Sorted… Everybody in this book is worried about what "sort" of people they are and with whom they belong. Often, characters make themselves feel better by labeling the opposing side as the "wrong sort" or "riffraff."
You might belong in Hufflepuff, Where they are just and loyal, Those patient Hufflepuffs are true And unafraid of toil… (7.33)
When the Sorting Hat describes the different houses, it emphasizes Hufflepuff's loyalty. Students in other houses may be braver, or cleverer, but the Hufflepuffs are "loyal" and "true." Some of the other Hogwarts kids could learn a lot from them.
Don't you care about Gryffindor, do you only care about yourselves, I don't want Slytherin to win the house cup, and you'll lose all the points I got from Professor McGonagall for knowing about Switching Spells. (9.132)
Hermione proves her loyalty to Gryffindor while simultaneously questioning Ron and Harry's – a comparison made neater by the fact that they share their house. Hermione doesn't help her case by mentioning the points she's gotten for studying, but she's wrong when she accuses the two boys of "only car[ing] about [them]selves."
"I went looking for the troll because I – I thought I could deal with it on my own – you know, because I've read all about them."
Ron dropped his wand. Hermione Granger, telling a downright lie to a teacher? (10.142-143)
Although Ron had insulted her earlier, Hermione shows her loyalty to him and Harry – and to their house – by lying to McGonagall about trying to find the troll. She explains it later as a responsibility to stand up for them just as they stood up for her, by coming to warn her about and defend her from the troll. This show of loyalty is, in part, what makes them such good friends later.
"Very well," Snape cut in. "We'll have another little chat soon, when you've had time to think things over and decided where your loyalties lie." (13.114)
Here, Snape is taunting Quirrell, trying to provoke him into revealing whether he knows how to get past Fluffy or not. Snape does this by questioning Quirrell's loyalty. Harry overhears this and wrongly suspects Snape of evildoing, but we can totally see why Harry would think that.
Malfoy told Madam Pomfrey he wanted to borrow one of my books so he could come and have a good laugh at me. He kept threatening to tell her what really bit me – I've told her it was a dog, but I don't think she believes me – I shouldn't have hit him at the Quidditch match, that's why he's doing this. (14.105)
In a double dose of faithfulness, Ron is being loyal to Harry and Hagrid by not revealing to Madam Pomfrey what really bit him. But he's also paying for the loyalty he showed to his family and friends when he tried to beat up Malfoy for insulting them.
Only Ron stood by him.
"They'll all forget this in a few weeks. Fred and George have lost loads of points in all the time they've been here, and people still like them." (15.20-21)
Here, Ron shows temporary and long-term loyalty to Harry, supporting him in a tough moment by acting like his friend – at a time when no one else wants to be – and encouraging him that, down the road, people will forget about these lost points. He argues that if Fred and George can keep their friends after losing points time and time again, that Harry should be able to also.