Why are we weigh'd upon with heaviness, And utterly consumed with sharp distress,
Now the sailors start a new stanza (labeled part "II" in the "Choric Song"). Right away they switch from talking about their beautiful new home to complaining about how hard life is.
Basically, their problem is that they feel bummed out all the time—not just sad ("weighed down with heaviness"), but also upset and stressed out ("utterly consumed with sharp distress").
While all things else have rest from weariness? All things have rest: why should we toil alone,
Apparently these (slightly whiny) sailors feel like everything else in the world gets to rest, while they are the only ones who have to labor and work ("toil").
This is just another effect of the Lotos. It makes rest look great, and any kind of work look awful. Again, be sure to notice the focus on words relating to tiredness and sleep here (e.g., "rest" and "weariness").
We only toil, who are the first of things, And make perpetual moan, Still from one sorrow to another thrown:
In these lines, we start to see that these sailors aren't just feeling sorry for themselves. They're actually complaining about how hard life is for all of mankind.
They think of mankind as the "first of things" (meaning the best, the first in line, the most important). Ironically, though (given that we're the first among all living things), we're also the only things on earth that have to work ("toil"). They also think that we're the only living things that experience sadness and express our sorrow ("make perpetual moan").
We could probably have an interesting talk about whether any of this is true: are humans first? Are we the only animals that feel sorrow? But you get the point, though. These guys are straight-up hating life.
Nor ever fold our wings, And cease from wanderings,
A lot of the imagery in this poem is about wandering versus being at home (check out lines 44-45, for example). These sailors are tired of wandering, and want to rest, the way other things in this world do.
To get that idea across, they use a metaphor, imagining that they are birds that can fold up their wings and sleep.
Nor steep our brows in slumber's holy balm;
In this line, the tired sailors fantasize about being asleep. They imagine that sleep would be a cure for all their misery.
They use a metaphor to compare sleep to a "balm" (a healing cream or ointment) that they could soak ("steep") their foreheads ("brow") in. Yuck. When you break that one down it doesn't sound do great, does it? Sleep is wonderful… like soaking your forehead in ointment? Count us out.
Nor harken what the inner spirit sings, "There is no joy but calm!"
These poor guys just can't get any rest. They imagine that their souls are telling them to be calm, to rest, to relax. They think that's the only way to be happy, to feel joy. But they can't do it—as humans they feel condemned to work and suffer instead of resting.
This obsession with resting and sleep is, from the outside, a little weird. There's lots of joy in life that isn't calm: playing with your kids, climbing a mountain, running a marathon (okay maybe that's a little too much work, even for us). The point is that these guys are under the influence. The Lotos has skewed their reality, and made them hate movement and love rest.
Why should we only toil, the roof and crown of things?
Now the boys on the beach finish off the second stanza of the choric song. They end their rant about how cranky and tired they are by asking why the best creatures in the world should be the only ones who have to work. The "roof and crown" are two metaphors for mankind's position at the top of creation (and the food chain).