The major fact about women's sports and physical education during the Antebellum period is that there was very little attention paid to it. The only real movement towards promoting fitness for women was done by activists such as Catharine Beecher.
Beecher was not a feminist by today's standards. She believed that the proper role for women was a nurturing one. They should be either wives and mothers or teachers. However, Beecher did believe that women should be in better physical condition than they were. She believed that this would enable them to do a better job of fulfilling their proper roles in society. This would help to improve the society as a whole.
With this in mind, we can say that what attention there was to women's fitness came about because of the desire to perfect society that was a major part of the 1830s and 1840s. Reformers like Beecher wanted to create a better society. To Beecher, at least, women who were more physically fit could do a better job of this.