Why was Kit angered when Dr. Bulkeley referred to Mercy as weak and afflicted?

Kit is angry at Dr. Bulkely’s prayer because she does not consider Mercy afflicted. 

Mercy is weak, but she doesn’t let that stop her.  She just does as much as anyone else in the household, and with patience too.  This is why Kit is angry when Dr. Bulkeley calls attention to her weakness.  

After a few days in this household Kit had ceased to be aware of Mercy's lameness. No one in the family ever referred to it. Mercy certainly did not consider herself afflicted. She did a full day's work and more. (Ch. 6)

Kit really admires Mercy, because she finds the work difficult even though she is healthy.  Mercy is patient enough to help her with it, and teach her how to do everything.  Mercy does this and her own work.

Mercy is not out of the woods yet though.  Later, she comes down with a terrible fever.  Her already weakened state makes this even more dangerous. 

Dressing rather shakily, Kit was compelled to ask Mercy's assistance with the buttons down her back, and was shocked when her older cousin suddenly bent double in a violent fit of coughing. Kit whirled round on her. (Ch. 17) 

Judith and Kit had already been sick.  Kit’s constitution was stronger than the colonists’ because of her time on Barbados.  Mercy was the one they had to worry about, however. 

Fortunately, Mercy recovers from her fever.  She marries John Holbrook, who is perfect for her calm and gentle personality.  Judith marries Wlliam Ashby, who had been courting Kit, but Kit marries Nat Eaton instead.  Everyone has a happy ending.