Her husband has not yet reached the age of retirement, and I suppose Norma is about the same age as him. .
Norma has gotten fatter and fatter over the years, and her family has started to loathe her because of her appearance, and I think of them as very superficial. They seem as if they only care for showing off what they have got: "At breakfast next morning June gave her mother instructions to empty "her junk room" because it would be just the right place to display the presents (p. 5, l. 52-53)". This superficial side of the family is something Norma is well aware of: "Colonel, do you think it acceptable practice to ask only the useful and or decorative to your wedding? (p. 4, l. 12-13)".
She has had to put up with harsh words and unfriendly voices in the house for years, and she has not gotten to display or tell about what really matters to her - no one wants to listen to what she has to say. I think the reason to why she is more attached to her cat than to her family is because she sees herself in it. It has visual outer "flaws" like her. But when she meets Arthur she comes out of her shell. She realizes that it is no use pretending to be someone else, and Arthur makes her see the world from a whole new perspective. His values make more sense to her, and she is more comfortable around him, because she knows that he does not judge on looks, and that he sees her for who she really is. His values are in a way more humane.
Despite them being complete opposites there is a certain attraction between them from the very first time they meet. This is where the old proverb comes in - "Opposites attract": He is very thin whereas she is very fat; he is interested in philosophy and she in English literature. I believe these last two contrasts to be the lead motives in the story. Philosophy is where you concentrate on relative things that are not visible to the human eye. For instance: Do we know for sure that we truly do exist? Perhaps reality is just something we imagine to be true.