Answer and explanation:
Up until this point of the plot in "Pride and Prejudice" by Jane Austen, the main character Elizabeth is still not at all fond of Mr. Darcy. She has the chance to meet his wealthy aunt and her daughter, Miss de Bourgh - Mr. Darcy's cousin and, supposedly, the one promised to marry him.
The reason why Elizabeth rejoices in Miss de Bourgh's sickly appearance is that she thinks Mr. Darcy is quite boring and irritating. Although she recognizes his intelligence, being mistreated by him in the past has left quite an impression on Elizabeth. She sees his marrying Miss de Bourgh as his deserved fate - sort of a punishment for his ill-tempered personality.
As we know, however, Elizabeth and Mr. Darcy end up falling in love. She also realizes that much of her former opinion of him was based in prejudice.