Some proposed brain weight is to be considered as a ratio of cc of brain per kg of body weight, and in such way, female and male brains won't differ. I have no data to say if this hypotesis is right.
What is quite sure is that a woman, after pregnancy, delivery, and breastfeeding, has a noticeable reduction, as measuerd by MRI, in some specific brain regions, shrinking that is long-lasting.
The functional meaning or translation, if any, of this finding, is unknown to me.
I met a man, who probably for issues of 'provocation', or obtaining support from someone he considered very old fashioned, used saying that: 'Women lack one brain convolution'. Hard 'joke'!
Human being is different from other species not only by brain quality, but in many other social and developmental aspects. Anybody can read a famous book :MEN ARE FROM MARS, WOMEN ARE FROM VENUS - by John Grey. I felt the points discussed in the book very much logical and right. Experts may comment.
I do not know, maybe it's more efficient. I would like to ask if there are other species in which to be bigger is the brains of females than that of males. If I can afford a joking answer perhaps the women's brain is smaller so as not to put too much trouble on us men, that is, to not obstruct the dominant male figure.
Really not only brain size, but in almost cases men body as all is bigger than that of women, it is naturally based fact(s). Recommended dear Dr. Arvind Singh and Dr. Houda Kawas, outstanding contributions.