Women have rounder-looking eyes with narrower fissures, but only in Europeans. Eyes are not sexually dimorphic in other human populations. (Petr Novak, Wikicommons)
The exposed white of the eye is larger in men than in women among Europeans but not in other human groups. This sexual dimorphism is due to the white of the eye being more horizontally exposed in men, with the result that female eyes look rounder. In addition, eye fissures are narrower and less rectangular in women (Danel et al. 2018; Danel et al. 2020).
This is analogous to what we see with eye color and hair color. Eyes are brown in most humans with the exception of Europeans, whose eyes may also be blue, gray, or green. Hair is black in most humans with the exception of Europeans, whose hair may also be blonde, red, or brown. In both cases, the palette of colors is more evenly balanced in women than in men. Women are less likely to have the more common hues, like blue or brown eyes and black hair. Conversely, they are more likely to have the less common hues, like green eyes and red hair.
There is no common genetic cause of these sex differences in eye morphology, eye color, and hair color. The genes are different in each case. The common cause seems to be some kind of selection among ancestral Europeans. Something favored the reproduction of women with rounder-looking eyes and less common eye and hair colors.
Was that "something" a someone? Were men selecting women through a process of sexual selection? That has been my explanation: in northern Eurasia until the end of the last ice age, women outnumbered men and had to compete for them, as a result of high male mortality and the high cost of polygyny. There was thus strong selection for women with an eye-catching appearance, and this selection ultimately changed the appearance of both sexes. The new phenotype eventually died out in northern Asia but survived in parts of Europe, which had a larger and more continuous human presence. It then spread throughout the rest of Europe almost at the dawn of history (Frost 2006; Frost 2014; Frost et al. 2017).
Danel et al. (2020) consider this explanation but reject it because female eye morphology does not correlate with two other aspects of female attractiveness: face shape and facial averageness. That lack of correlation, however, simply shows that each of these aspects has different constraints on the direction of sexual selection:
Eye morphology - the direction of sexual selection seems open-ended. Women are more attractive if they have rounder eyes.
Face shape - the direction of sexual selection goes into reverse beyond a certain point. Women are more attractive if they have smaller chins and smaller noses, but only up to a certain point. Excessively small chins and noses are not attractive either.
Facial averageness - the constraints are again different. Women become less attractive on each side of a narrow median.
References
Danel, D.P., S. Wacewicz, Z. Lewandowski, P. Zywiczynski, and J.O. Perea-Garcia. (2018). Humans do not perceive conspecifics with a greater exposed sclera as more trustworthy: a preliminary cross-ethnic study of the function of the overexposed human sclera. Acta Ethologica21: 203-208.
https://doi.org/10.1007/s10211-018-0296-5
Danel, D.P., S. Wacewicz, K. Kleisner, Z. Lewandowski, M.E. Kret, P. Zywiczynski, and J.O. Perea-Garcia. (2020). Sex differences in ocular morphology in Caucasian people: a dubious role of sexual selection in the evolution of sexual dimorphism of the human eye. Behavioral Ecology and Sociobiology 74(115)
https://doi.org/10.1007/s00265-020-02894-1
Frost, P. (2006). European hair and eye color - A case of frequency-dependent sexual selection? Evolution and Human Behavior 27(2): 85-103.
https://doi.org/10.1016/j.evolhumbehav.2005.07.002
Frost, P. (2014). The puzzle of European hair, eye, and skin color. Advances in Anthropology 4(2): 78-88.
https://doi.org/10.4236/aa.2014.42011
Frost, P., K. Kleisner, and J. Flegr. (2017). Health status by gender, hair color, and eye color: Red-haired women are the most divergent. PLoS One 12(12): e0190238.
https://doi.org/10.1371/journal.pone.0190238