However, JA is saying that although it is not fair to ridicule someone based on their size, people tend to do it.

Also, "large fat sighings" may or may not be a pun on Mrs. Musgrove's size, but may just refer to the loud and excessive manner of expressing her sorrow. I am not saying this to try to defend JA, but perhaps we should give her the benefit of the doubt here. For, though we do know her to have used caustic wit in her personal letters, she had not done so in her novels before.