"White Tears" is a phrase used to describe what happens when certain types of white people (particularly Americans) either complain about nonexistent racial injustice, or are upset by by the success of a person of color at the expense of a white person. 
In the media
Fisher v. University of Texas
A prominent example of this phenomenon is Fisher v. University of Texas (2016), a court case involving Abigail Noel Fisher (a white woman with slightly above average test scores) being denied admission to the University of Texas. She along with another woman filed suit, alleging that the University had discriminated against them on the basis of their race.  Fisher had a grade point average of 3.59 (adjusted to a 4.0 scale), ranked 82 out of 674 students, and 1180 out of 1600 on SAT.  Fisher claims, "There were people in my class with lower grades who weren't in all the activities I was in, who were being accepted into UT, and the only other difference between us was the color of our skin."  Based on court findings, the university offered provisional admission to Forty-seven students (five were black or Latino, and Forty-two were white). There were also 168 black and Latino students with grades as good as or better than Fisher's that were also denied entry into the university the same year she applied. 
Lake Merritt (2018)
In May 2018, a family in Oakland, California, attempted to barbecue at Lake Merritt Park. A white woman (concerned with the fact that the family was using a charcoal grill in the wrong area for grilling) proceeded to call the cops. The cops arrived two hours later they arrived. The woman approached the cops crying, “After two hours, I just called back the nonemergency line, and in the interim these people came up and started harassing me, physically pushing me.”  Footage of the incident shows no evidence of such physical interactions. In the aftermath, many memes began to surface. 
In the Summer of 1955, Emmett Till (a 14 year old black boy from Chicago) went to Mississippi to spend summer with his family. He was accused of wolf-whistling at a pretty white woman. The white woman Carolyn Bryant accused Till of flirting with her, and this led to her husband Roy Bryant and his half-brother J.W. Milam murdering Till and dumping him in the river. The two were acquitted of all charges in court. Bryant later disclosed that she had fabricated testimony that Till made verbal or physical advances towards her in the store.