I measure every Grief I meet
The speaker tells us about a strange habit of hers: she's a fan of measuring grief. Now we don't know if that entails scales, rulers, or graduated cylinders. But we do know it means she does a bit of comparison, because she tells us that she compares the grief of others to her own. While she observes these people, she always returns to herself and to her own sadness and grief. So in addition to guessing about other people, she also compares herself to them, asking "Is this person as sad as me?" and "Have they felt sad as long as I have felt sad?"
Next, the speaker talks about people who seem to get over their grief. She's kind of skeptical about this, and she suggests that they are probably faking it. After this, the speaker starts to list some of the causes of grief—some people are grieving the death of a loved one, some are sad because they want something they don't have, others experience a general sort of "despair."
At the end of the day, the speaker never really gets the answers to the questions she asks, and she also may never know why someone is sad, but that doesn't seem to matter to her. The simple act of noticing that someone else is sad seems to be enough to make her feel better, and that's kind of the point.