(noun) a staff for holding the flax, tow, or wool in spinning OR relating to women
the only rel chink in the operative's distaff persona
on Steeply's feminine disguise
uncomfortably weighted against the distaff
I assume in this case it means: weighted against the woman (i.e., Anabel)
Women were spinsters before the word became pejorative, when distaff meant the female side of the family.