Esther apologizes for spending so much time talking about herself. To which the answer is obviously "Huh?" – since in reality she is constantly leaving herself out or putting herself down. So this is just more of that.
Richard and Ada are falling in love. No worries, back then it was totally cool for cousins to get together. And it doesn't seem like they're first cousins or anything.
In any case, Esther thinks it's adorable. Such a cute couple!
But she is also worried about Richard's idiotic rationalizations about money. He is not a saver.
After some time, Jarndyce gets a letter and is psyched to announce that his childhood friend Lawrence Boythorn is coming to visit. They met at school, when Boythorn saved Jarndyce from some bullies. (Brain snack: see Dobbin and George Osborne in Vanity Fair for an identical meet-cute bromance.)
Jarndyce says Boythorn is large, loud, brave, very emphatic, and generally awesome.
Boythorn arrives late and bursts into the house yelling about some jerk who gave him bad directions.
He alternates between saying that things are amazingly awesome and that they're terrible and whoever is responsible for them should be shot. Jarndyce clearly loves him.
At dinner there's more of the same, except now Boythorn's pet, a tiny yellow bird that's so domesticated it doesn't need a cage, sits on his head and eats out of his hand.
So Boythorn clearly has a lot of bark and not much bite.
Also, it turns out that he is Sir Leicester Dedlock's neighbor, and they are constantly suing each other and fighting over the borders between their estates.
After dinner Esther notices how Boythorn watches Ada and Richard.
Later she asks Jarndyce whether Boythorn was ever married. Jarndyce says no, but Esther guesses he was supposed to be married. She's a smart cookie.
It turns out that something happened to Boythorn's fiancée, and he has never been the same since. Esther thinks about this, then dozes off and dreams about her Aunt's house.
The next morning Guppy from Kenge and Carboy's office swings by Bleak House. Esther recognizes him as the young man who helped her in the court building the first time she came to London.
Guppy hems and haws a bit, and then...proposes marriage to Esther! Readers everywhere say, "what the...?"
Esther lets him down as gently as possible. Guppy says that despite her saying no, he will promote her interests as best as he can. Whatever that means.
Esther gets rid of him as quickly as she can, then goes upstairs. Thinking about his proposal first makes her laugh. Then it makes her cry. Aww.