This expression means to treat someone with disdain bodering on contempt. This is an especially appropriate phrase when the person is outside of one’s group. Why shiroi (white) eyes? One theory is that eyes without pupils would have a cold, ghostly look analogous to a scornful rebuke.
A: Kondo hikkoshite kita Inoue-san ne. Ano hito wa honto no okusan janakute, aijin na n datte. Sore ga shirete kara mawari no shufu wa minna shiroi me de mihajimeta yoo yo.
A: You know the Inoues who just moved in? I hear Mrs.Inoue is not the wife, but a mistress. Once the news spread, housewives in the neighborhood began to look at her coldly.