Just before we are told that Hazel has tears running down her cheeks, we are told that her "fourteen-year-old son, Harrison," has been taken away by "the H-G men." This sudden loss of her son must of course be very traumatic. We are also told, however, that Hazel is unable to "think about it very hard" because she has "a perfectly average intelligence, which meant she couldn't think about anything except in short bursts."
The fact that Hazel cries implies that she has a profound sadness inside of her, and the fact that she doesn't know why she cries implies that she does not have the mental capacity to process or understand this sadness. It is significant too that Hazel is watching the television when she is crying. The television is a distraction. It is there to stop her thinking. Instead of being able to process her sadness, her attention is distracted by the spectacle of the ballerinas on the television screen. Indeed, Hazel comments that, "That was a real pretty dance, that dance they just did." This rather anodyne, inane comment emphasizes her inability to think beyond what is immediate and self-evident. As Roald Dahl once wrote, the television "rots the sense in the head" and turns one's brain "as soft as cheese." This seems to be Vonnegut's opinion of television too.
The fact that Hazel is sad and unable to think for herself reflects what has become of the United States of America in Vonnegut's dystopian, satirical story. The people in the story have been, for the most part, reduced to pitiful, unthinking, passive, and emotionally repressed nonentities.