I happened to catch just a couple of minutes of the NPR program This American Life one day and the subject seemed to be analyzing the number of potential mates for a person in a reasonably sized city. The (student?) investigators would ask various people what characteristics they considered essential for a mate and them try to figure out the likely numbers. One woman they asked said: "he just needs to be taller than I and smarter."
Given that she was tall and a Harvard physics professor, said our investigator, her odds didn't look good.
I was more interested in her choices. Why would those particular characteristics be crucial? The "taller" characteristic in particular seemed pretty superficial to me for a physics professor, and the "smarter" part was odd too. As a Harvard physics prof, I thought, she must have nearly always been smarter than all the males she knew. I was also struck by the fact that it was relative rather than absolute height and smartness that seemed crucial.
It seems though, that this sort of thing is pretty common, at least when answering questions rather than actually making a choice. Many women do indeed want a husband taller than they are. Obviously this limits the choices of a 5' 11" woman a lot more than those of one who is 5' 2".
So what about personality, character, and sense of humor? Shouldn't these things be a lot more important than a superficial quality like height? In practice, they are, I think, but the fact that many women mention it suggests some evolutionary basis.
So why should relative height be important to women? If height is such a big deal, why aren't all men 6' 11"?
At the primitive evolutionary level, height might be a badge of good health or even of high status (high status children presumably getting better nutrition). Height is definitely not an unmixed blessing of course - even if you assume that comfort in airline coach seating was not an evolutionary priority when these traits supposedly evolved. Tall people are shorter lived, need more food, and don't maneuver well in tight spaces.
I've got to say though, that being a moderately tall man (6'-3") did definitely not lead to the girls flocking around me in high school. Maybe the nerd factor was dominant here. On the other hand, Wilt Chamberlain, the 7' 1" basketball superstar claimed to have had sex with 20,000 different women, which would amount to roughly three a day for twenty years.