I definitely agree with you that there are clearly closer bonds within the Stark family. For example, when Jon thinks of fond memories from home, sometimes only Arya is involved, but in many of them its always "Robb, Bran, Arya" and he thinks how Bran and Arya played together like him and Robb before them. Its really cute! I think the Bran x Arya relationship is underrated, they were pretty close as well. Rickon was too young to form those bonds, which breaks my heart, the poor baby.

This quote?

I love it. It’s so cute. It also mirrors a quote of Arya’s I have further down.

Yeah, I once catalogued Jon’s moments when he thinks of his family, and unless it’s every single child in the Starks, it’s mainly just Arya, Bran, and Robb (though Robb references lessen a bit post-ASoS and Ned was included in AGoT.) But that makes sense because the three of them were also his three goodbyes before leaving Winterfell. 

There are several other cute ones, but I’ll leave that for another post.

Well, this mirrors many real families. Even in close families, there tends to be people with closer bonds because of things like similar interests. Age is also a huge factor. Jon is way closer with Robb than Rickon for instance because he grew up with Robb, and Rickon was too young for him to form a bond with.

But about Bran x Arya. Well, I’m glad you asked because I have a bunch of feelings on the subject. First, you’re right, they are a highly underrated relationship.

There’s some great parallels to start with.

They’re both climbers:

They’re not fans of romantic stories:

 They both have darkness as a theme that their teachers tell them will give them strength/guide them:

“How long must I be blind?” she would ask. “Until darkness is as sweet to you as light,” the waif would say, “

“You must now walk in darkness until you see the way” [the Kindly Man tells Arya] Arya, ADWD

They’ve both met at least one of the Children of the Forest despite them being so rare now:

They are also the most accomplished skinchangers so far, the youngest two POVs, and deal the most with wolves (although Jon’s up there.)

But about their actual relationship. Well, for starters, Bran likens someone he has great respect for to Arya:

He’s highly complimentary of Arya here since the idea of women being on par with men in terms of running, fighting, and throwing is unusual in such a patriarchal society. But also because of Bran’s feelings for Meera.

Bran thinks very highly of Meera, so the comparison of the two girls in Bran’s life is great praise.

Also, I like this bit:

Bran seems to really know Arya here, especially considering what we see of Arya/Elmar’s interaction. 

And one of my favorite things is how Bran sees Arya all the time now. There’s him seeing Arya in Meera above but also

Bran sees Arya in Leaf.

and he sees Arya in Lyanna. Another great thing of that second quote is that it alludes to how Bran and Arya used to play. Bran even thinks “if the girl was Arya, the boy was Bran himself” and that “Arya never beat me playing swords”, which means that they must have played swords a fair amount together. This is also interesting because people tend to see people they miss or are thinking about in others. 

And on Arya’s side there are some good moments as well.

“Not for a long time, sweet one,” he told her. “He needs to win his strength back.” Arya bit her lip. “What will Bran do when he’s of age?” Ned knelt beside her. “He has years to find that answer, Arya. For now, it is enough to know that he will live.” The night the bird had come from Winterfell, Eddard Stark had taken the girls to the castle godswood, an acre of elm and alder and black cottonwood overlooking the river. The heart tree there was a great oak, its ancient limbs overgrown with smokeberry vines; they knelt before it to offer their thanksgiving, as if it had been a weirwood. Sansa drifted to sleep as the moon rose, Arya several hours later, curling up in the grass under Ned’s cloak. All through the dark hours he kept his vigil alone. When dawn broke over the city, the dark red blooms of dragon’s breath surrounded the girls where they lay. “I dreamed of Bran,” Sansa had whispered to him. “I saw him smiling.”

“He was going to be a knight,” Arya was saying now. “A knight of the Kingsguard. Can he still be a knight?” AGoT

I love how Arya is asking after Bran’s dreams. She knows Bran wanted to be a knight and wants to know if he still can.

And this is the sweetest memory of all the Stark kids (sans Rickon who had not yet been born) but has some close Arya/Bran bits:

Robb took them all the way down to the end, past Grandfather and Brandon and Lyanna, to show them their own tombs. Sansa kept looking at the stubby little candle, anxious that it might go out. Old Nan had told her there were spiders down here, and rats as big as dogs. Robb smiled when she said that. “There are worse things than spiders and rats,” he whispered. “This is where the dead walk.” That was when they heard the sound, low and deep and shivery. Baby Bran had clutched at Arya’s hand.

When the spirit stepped out of the open tomb, pale white and moaning for blood, Sansa ran shrieking for the stairs, and Bran wrapped himself around Robb’s leg, sobbing. Arya stood her ground and gave the spirit a punch. It was only Jon, covered with flour. “You stupid,” she told him, “you scared the baby,” but Jon and Robb just laughed and laughed, and pretty soon Bran and Arya were laughing too.

The memory made Arya smile, and after that the darkness held no more terrors for her. AGoT

Arya uses this memory to keep her calm and unafraid right after everything becomes chaotic in her life- this is just after she killed the stableboy. I love picturing a three year old Bran clutching Arya’s hand because he’s afraid and then Arya getting defensive of him. “You scared the baby.”

Another reminder that Arya and Bran used to play together. But also, I think it’s cute that Arya wonders if Bran is sad. She’s worried about him even though she’s in a horrible position herself at the moment, stuck alone in Flea Bottom without food or shelter or any sort of idea what’s going on.

And another quote to indicate that Arya and Bran played together and were probably up to the most mischief in the Stark household actually.

I think that Arya and Bran had a great relationship, which shows through in the text, and an underrated one. Bran and Arya are portrayed as each others’ primary playmate (likely because they are close in age,) enjoyed similar things like sword playing and climbing and snowball fights, and have some interesting parallels (like their mutual dislike of romantic stories and their themes of darkness as given by a mentor in ADWD and just by being the most accomplished skinchangers so far in the Starks.)