Grief. It's right there in the first line: "I measure every Grief I meet." But this poem isn't just about suffering and being mopey about it. Even though the speaker returns ultimately to her own suffering, the attention to the sadness of others and to different kinds of grief keep the poem from becoming one giant sob fest. There is a sense of sympathy here that makes the poem about a more universal sense of suffering, rather than one's own, private bummers.
The speaker uses the suffering of others to make herself feel better, which is just plain tacky.
The speaker's ability to find comfort in the suffering of others is nothing but a way to hide that she's a pessimistic moper.