What is the "infinitely delicate balance" that the author refers to in paragraph 66?

In the stolen party.

The moment of balance is between Rosaura's persona at the party and the fact that she is the daughter of the housekeeper. When Señora Ines holds out the money to Rosaura, she is reminding her that she isn't like other children. If Señora Ines gave Rosaura anymore than two dollars, like a gift, it would mean they are equal, and Rosaura was equal to the other children.

Answer:The infinitely delicate balance at that moment is the balance between Rosaura's persona at the party and the fact that she's the daughter of the housekeeper. When Señora Ines holds out the money to Rosaura, she's reminding her that she isn't like the other children; she's the child of a servant.