Why do the Fosters live in such a big house?

The text does not directly address why the Fosters live in such a big house. It appears that the Fosters live in a big house as a matter of preference. Also, the Fosters' affluence provides them more choices in how they choose to live.
The text describes the Fosters' home as a large, six-story house in New York City. The house is located on East Sixty-second Street. The Fosters have four servants, and their home is said to be a gloomy place. The Fosters' only daughter lives in France with her husband and three children.
The text describes Mrs. Foster's preparation for her journey to France. Interestingly, her husband is not accompanying her on the trip. The house is said to have come alive as a result of the preparations for Mrs. Foster's trip. The butler has busied himself carrying down suitcases, while other servants are draping dust sheets over the furniture. The author hints that Mrs. Foster does not enjoy living in the big house with her husband. 

And now, lately, she had come more and more to feel that she did not really wish to live out her days in a place where she could not be near these children, and have them visit her, and take them out for walks, and buy them presents, and watch them grow. She knew, of course, that it was wrong and in a way disloyal to have thoughts like these while her husband was still alive.

Accordingly, although the Fosters live in a big house by choice, we know that Mrs. Foster feels lonely and yearns to be with her daughter and grandchildren.