How we cite our quotes:
To finish the interest of the story, the friendship between him and the Harvilles seemed, if possible, augmented by the event which closed all their views of alliance, and Captain Benwick was now living with them entirely. (11.12)
Most friends bond over fun activities, but here it's sharing bad experiences that brings the friends closer together. The shared memories of Fanny also seem a factor – together they can talk about a past that few others remember.
There was so much attachment to Captain Wentworth in all this, and such a bewitching charm in a degree of hospitality so uncommon, so unlike the usual style of give-and-take invitations, and dinners of formality and display, that Anne felt her spirits not likely to be benefited by an increasing acquaintance among his brother-officers. "These would have been all my friends," was her thought; and she had to struggle against a great tendency to lowness. (11.16)
Wentworth's close friends make it all the more apparent how much Anne lacks in this area: at this point in the novel all she has is Lady Russell, who's also kind of like her mom, and so it isn't really an equal friendship like Wentworth has with his brother officers.
But the remembrance of the appeal remained a pleasure to her, as a proof of friendship, and of deference for her judgement, a great pleasure; and when it became a sort of parting proof, its value did not lessen. (12.2)
For both Anne and Wentworth, respect is a key aspect of friendship – and so Anne interprets Wentworth's show of respect as a renewing of the friendship between them.