This source says that "broad" may be suggestive of broad hips or may refer to "abroadwife" for a woman away from her husband.
"O.E. brad, from P.Gmc. *braithaz (cf. O.Fris. bred, O.N. breiðr, Du. breed, Ger. breit, Goth. brouþs), of unknown origin. Not found outside Gmc. languages. Slang extension to meaning "woman" (1911) may be suggestive of broad hips, but it also may trace to Amer.Eng. abroadwife, for a woman away from her husband, often a slave. Earliest use suggests immorality or coarse, low-class women." http://dictionary.reference.com/browse/broad
In support of edmund80's post with another piece of info:
Slang extension to meaning "woman" (1911) may be suggestive of broad hips, but it also may trace to Amer.Eng. abroadwife, for a woman away from her husband, often a slave. Earliest use suggests immorality or coarse, low-class women. Because of this negative association, and the rise of women in athletics, the track and field broad jump was changed to the long jump c. 1967.
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