Dickinson wrote a lot of poems about sadness, but this little ditty stands out for two reasons. First, it addresses the sadness of people other than the speaker. Secondly, it lists different kinds of grief, rather than just sticking to a general one. This isn't all about death—it's about all different kinds of suffering, and how they connect to the greater suffering of the world.
Line 1: If you had to characterize how Dickinson describes grief in the first line, what would you say? She seems to be giving grief (which is an abstract concept) the properties of a physical thing, since it's something that can be measured, something with weight. So while she's not explicitly comparing grief to anything, we can say that she is using a sneaky metaphor, because she is suggesting that grief has physical properties like that of an object.
Stanza 4: In lines 15 and 16, the poem sets up a metaphor that compares a person's overall happiness or "life force" to oil in a lamp. Just as oil is required to cause the lamp to brighten, happiness is required to get someone to smile. The poem suggests that a grieving person's smile could never be real, because they have too "little Oil." When you think about it, the speaker pretty much engages in circular reasoning here, because she is assuming what she should be proving. How does she know that the person's smile isn't real? She doesn't, but she assumes so, because in her mind, sad people have "so little Oil" that any sign of happiness they produce must be fake. Could the speaker be projecting, possibly? Is this how she really feels inside?
Line 35: The very fact of knowing that other people have experienced grief gives the speaker a sense of "piercing comfort." Here the poem combines two terms that are opposites in order to reveal a strange paradox. "Piercing comfort"? That's an oxymoron. Why might comfort be piercing? It could be that since she's so used to being sad and uncomfortable that the experience of comfort comes as a complete shock to her system. Or, maybe the experience of comfort actually makes her uncomfortable, it pierces her, it's almost painful.