People get gray hair when they age, and hers was not the time when a woman would color that to look more attractive.  People often gain weight as they age, too.  The point is not so much that she got gray and fat, but the language the narrator uses this to describe it, which is the language of the grotesque.  "She looked bloated like a body long submerged in motionless water," the narrator says. All of these words describe a corpse, not a person, and a frightening one, left abandoned after drowned, years ago.  And she, in a way, drown, in a lack of love, and an abundance of paternalism.

Emily is plagued by isolation and loneliness.  She is set apart from the town as an "other,"; her father was a well-to-do military official during the Civil War and the famiy enjoyed privledges (like not paying taxes) that ordinary people did not.  She perhaps was not particularly attractive and probably shy, which didn't help matter any. 

The weight gain and gray hair are signs of depression.  The town ignores her problems and only comes to understand the depth of her psychological trauma after she dies.