At the turn of the century, unwed pregnancy was seen as a scandal, something unacceptable in society and that made both the mother and the child despised by everyone and even by the family itself. Currently, unwed pregnancy is seen with less hostility.
As a single mother, Grace would have faced a very difficult future. She could be rejected by the family, be frowned upon in society and not be able to support herself and her son anymore, because in a factory she would hire a single mother.
By reading the letters, we can see that Grace was very afraid of being a single mother, because she knew it would be very difficult. For this reason, she begged her b0yfriend to assume the child's paternity.