Anthropologist Peter Frost writes:
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).I don't know whether he is right or not, but has an impressive amount of evidence in support. He mentions that there are naysayers, but I don't know of a viable competing theory.
This is analogous to what we see with eye color and hair color. ...
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).