Stanza 1 Summary

Get out the microscope, because we’re going through this poem line-by-line.

"Dream Song 29"

The title of this one, as is often the case with poetry, is super-important. It gives us a couple key pieces of information that will help us as we move into the poem.
First, we have that word "dream." We need to keep this word in mind as we work through the poem. The dream world is a slippery thing. Sometimes things seem very real, sometimes they seem completely surreal, other times the dream world is a freaky combination of reality and totally unreal components. Expect things to get a little freaky in this one.
Second, it's a song. Songs use sound (music) to create feeling and meaning. If the song has lyrics, then the emotional content comes through a combination of sound and words. The point is we shouldn't expect this thing to read like standard text. It's using sound and words in a more lyric way. (No, not that kind of lyric.)
Lastly, we have the number 29. This tells us that there is probably a whole mess of these songs. In fact, there are close to 400 of them. See, it could be worse. You could have been assigned all 385 Dream Songs. If you were, we're sorry.

There sat down, once, a thing on Henry's heart

The first line of "Dream Song 29" sounds a little like the beginning of a fairytale or a children's story. It has a certain once upon a time feeling. True, it could have something to do with the word "once." But the line also feels fairytale-ish because it is very rhythmical. It has a sort of bouncy, children's story feel. (Check out "Form and Meter" for more on the poem's rhythm.)
Line 1 also introduces us to the character of Henry. Hi, Henry.
It is a strange description—something "sat" on Henry's heart. But we understand. We understand that Henry is sad because we are familiar with expressions like with a heavy heart or the idea of having a heavy heart. So, something is making Henry sad. It sits on his heart and makes him feel the weight of the sadness. It sounds like Henry could use a hug.

só heavy, if he had a hundred years
& more, & weeping, sleepless, in all them time
Henry could not make good.

First things first: yes, that's an accent mark over the "O" in "so." So… what's the deal? Well, Berryman was probably just trying to help us understand how he wanted the word to be read. He wanted it to be stressed. If you listen to the man himself read the poem you might hear what he was after.
So, the thing sitting on Henry's heart, the thing making him sad, is heavy—sooo heavy that he can't shake it. Even if he had a really long time and a good cry, he still wouldn't feel better: "Henry could not make good."
The syntax in line 3 seems a little unusual. Instead of saying "In all that time," he says, "in all them time." Weird, right? This kind of irregular syntax pops up from time to time in The Dream Songs. Berryman used these irregular phrases to express various dialectical influences—everything from a kind of exaggerated African-American dialect, common in minstrel shows from the days of vaudeville, to child-like phrases and slang. In #29, the irregular syntax heightens the sense of things being a little off, not quite right, as they often are in dreams.
And what about those ampersands? You know, those squiggly things that mean "and"? Berryman used these throughout The Dream Songs. They give the poems a more casual feel—like something just dashed off (perhaps after waking up from a dream). The poems feel more in the moment. They give the reader the sense that these lines are unrevised and unedited.

Starts again always in Henry's ears
the little cough somewhere, an odour, a chime.

Even when Henry thinks the sadness is starting to lift, it "starts again." It starts small, like an annoying noise or an unpleasant smell.
But these small annoyances signal that the sadness remains, ready to plop down on Henry's heart for a nice long sit.
Berryman really lets us feel the creeping sadness by using a lot of sensory descriptions: feelings, smells, sounds. These kinds of descriptions help to pull us into the poem, help us to feel what is being described.
Finally, we get some haphazard rhyming in this stanza ("years" and "ears," "time" and "chime"). For more on that technique, check out "Form and Meter."