Yet the moth has trim, and feistiness, and not a drop of self-pity. (4.7-8)
Our speaker hasn't directly addressed the idea of sadness yet, but we get a glimpse of her feelings on the matter here. She clearly admires the moth, in part because it doesn't have the slightest bit of self-pity. Since the lack of self-pity goes along with lively attributes like "trim" and "feistiness," there's the suggestion that self-pity goes along with a certain dullness or un-liveliness.
my mother, alas, alas, did not always love her life, heavier than iron it was as she carried it in her arms, from room to room (5.5-8)
This image is really powerful and shows us the weight of sadness as our speaker sees it. Her mother is an example of how not to live one's life. Iron is pretty heavy, so if her mother's sadness made her life heavier than iron, well, that's pretty sad.
oh, unforgettable! (5.9)
This line makes it clear that this unhappiness of her mother's was related to some bad memories, something she couldn't forget. Our speaker makes a pretty clear connection here between sadness and not being able to move on from the past, or what's lost.
But the iron thing they carried, I will not carry. (6.5)
Our speaker is determined not to repeat the mistakes her parents made. She explains that she loves and respects her parents, but she will not linger on their memory and will not mention them again. Why? Because to do so she would have to be in a state of constant mourning, which would keep her from connecting with the world.
The voice of the child crying out of the mouth of the grown woman is a misery and a disappointment. (9.1-3)
This, like that line "oh, unforgettable," seems to say that if we don't move on from past losses they will haunt us and make us miserable. In this case, this grown woman is still at the graveyard (to use our speaker's image), mourning some loss or hurt from her childhood.
Let grief be your sister, she will whether or no. Rise up from the stump of sorrow, and be green also, like the diligent leaves. (12.8-10)
Here our speaker acknowledges that we can't just not be sad, or not experience grief. So what then? It seems we should get to know it, let it come and be close to us, since we'll experience it no matter what. Our speaker seems to think that when you fight sadness, you just make it worse. So it's not just a matter of trying to deny its existence; you have to accept it, acknowledge it, before you can go about living your life. Of course, you could argue that the gap between the two actions she recommends here (letting grief be our sister and rising from the stump of sorrow) might be a bit of a leap for some of us.