"Thank you; for now we shall soon be acquainted, as I am authorized to tease you on this subject whenever we meet, and nothing in the world advances intimacy so much." (3.50)
Henry's ideas on friendship are closely linked to his sense of humor, which contrasts to some of the other views of friendship and 'intimacy' that we get in the book, namely those of Isabella.
Friendship is certainly the finest balm for the pangs of disappointed love. (4.6)
This is one of the best thematic statements in the whole text, since Northanger Abbey is not only concerned with romantic love, but with friendship as well. In fact, friendship might arguably play a more important role in the bulk of the text than romantic love.
The progress of the friendship between Catherine and Isabella was quick as its beginning had been warm, and they passed so rapidly through every gradation of increasing tenderness, that there was shortly no fresh proof of it to be given to their friends or themselves. (5.4)
Friendship has a lot to do with performance here, and it can be demonstrated or "proven" to others. The speed with which Catherine and Isabella pass through all the stages of friendship suggests that they are following some sort of prescribed, or set, route for being friends.
"There is nothing I would not do for those who are really my friends. I have no notion of loving people by halves, it is not my nature. My attachments are always excessively strong." (6.14)
Isabella's sentiments on friendship are a bit confusing. She is selfish, but her attachment to Catherine is, or appears to be, very strong. Isabella seems to hint that she has high expectations for friendships as she places an emphasis on people who are "really" her friends.
[…] having gone through the usual ceremonial of meeting her friend with the most smiling and affectionate haste, of admiring the set of her gown, and envying the curl of her hair, they followed their chaperons, arm in arm, into the ball-room, whispering to each other whenever a thought occurred, and supplying the place of many ideas by a squeeze of the hand or a smile of affection. (8.1)
This paints a nice picture of the affectionate friendship between Isabella and Catherine, but two words put a bit of a damper on things: "ceremonial" and "haste." It sounds like Isabella is rushing to do what's expected as a friend.
Catherine began to doubt the happiness of a situation which confining her entirely to her friend and her brother, gave her very little share in the notice of either. (10.9)
Catherine experiences the woes of being a third-wheel here, while Isabella and James come off as somewhat rude for ignoring Catherine.
Catherine thought this reproach equally strange and unkind. Was it the part of a friend thus to expose her feelings to the notice of others? Isabella appeared to her ungenerous and selfish, regardless of everything but her own gratification. (13.3)
Catherine begins to spot the contradictions within Isabella's statements, which leads her in turn to start doubting how good a friend Isabella really is.
A few days passed away, and Catherine, though not allowing herself to suspect her friend, could not help watching her closely. The result of her observations were not agreeable. Isabella seemed an altered creature. (19.1)
Notably, Catherine beings to actually watch and observe Isabella after growing suspicious of her, and she begins to see Isabella as she really is.
Isabella, on hearing the particulars of the visit, gave a different explanation. "It was all pride, pride, insufferable haughtiness and pride! She had long suspected the family to be very high, and this made it certain. Such insolence of behavior as Miss Tilney's she had never heard of in her life! Not to do the honours of her house with common good-breeding! To behave to her guest with such superciliousness! - Hardly even speak to her!" (16.1)
Here Isabella "proves" her friendship to Catherine by bashing Catherine's new friend, Eleanor Tilney, who was oddly quiet during Catherine's visit to her house. Isabella's tactics place her in a worse light than Eleanor, however.
Miss Tilney, whose trust in the effect of time and distance on her friend's disposition was already justified, for already did Catherine reproach herself with having parted from Eleanor coldly; with having never enough valued her merits or kindness [....] The strength of these feelings, however, was far from assisting her pen; and never had it been harder for her to write than in addressing Eleanor Tilney. (29.14)
Catherine's mature and meaningful friendship with Eleanor is highlighted here. Catherine pays attention to her friend's feelings, which shows growth on Catherine's part. And the fact that Catherine has trouble writing a sincere letter shows that she is moving away from the "ceremonial" and ultimately hollow friendship she had with Isabella.