I all alone beweep my outcast state, (2)
The speaker comes right out and says that he's a social outcast (although, we're never really sure why that is). Just in case we didn't get how lonely he feels, he says that nobody feels any sympathy for his situation, describing himself as "I all alone."
And trouble deaf heav'n with my bootless cries, (3)
In the first two lines, we learned how the speaker feels like a social leper. By the third line, he's all "Are You There God? It's Me, Margaret." In other words, he also feels isolated from God. His cries (a.k.a. prayers) go unanswered, and he's pretty bitter about it. And, he all but accuses God of being annoyed (or, "trouble[d]") with him. Plus, the fact that the speaker can't even come out and say God's name (he uses the word "heav'n") reinforces the idea that he is spiritually distanced from God.
And look upon myself and curse my fate, (4)
Hmm. This poem is all about the speaker's introspection. Translation: He's consumed with himself. Is that why he's "all alone" and isolated?