Symbolism, Imagery, Allegory
Unlike the other Aglionby boys, Adam doesn't wear snazzy or brand new outfits. Even when he's wearing his school uniform—which should be exactly the same as everyone else's—his clothes are noticeably shabbier. Like Ron Weasley from the Harry Potter series, Adam's secondhand clothes mark him out as the poor friend:
"God," Ashley remarked. She glanced at Adam. Her eyes didn't linger, but still, he remembered the fray on the shoulder of his sweater.
Don't pick at it. She's not looking at it. No one else notices.
With effort, Adam squared his shoulders and tried to inhabit the uniform as easily as Gansey or Ronan. (4.40-42)
Adam's frayed clothes are just another indicator that no matter how much he tries, he can't get on the same "level" as his friends. He may go to the same school, hang out with the same people, and even go on the same adventures, but he comes from a completely different background.
He feels inadequate even when he's at Aglionby with them, because he knows that he has to work three times as hard to even pay the tuition. He still retains his Henrietta accent and lives in a trailer park with his parents. The uniform sweater is just another example of how he's trying to fit in, but he can't quite be like his friends.