PEACHUM. For the villainy of the world is great, and a man needs to run his legs off to keep them from being stolen from under him. (1.3.215-217)
Peachum suddenly gets poetic on us, sharing his philosophy on life with a depressing hyperbole. His crazy image, of running your legs off to save them from being stolen, reveals his chaotic, dangerous image of existence.
PEACHUM. Once all are good His Kingdom is at hand
Where blissfully we'll bask in His pure light.
Let's practice goodness: who would disagree?
But sadly on this planet while we're waiting
The means are meager and the morals low. (1.3.247-251)
And moving on to irony, Peachum refers to the Church's version of life, in which God's Kingdom will exist on earth and everything will be peachy. He contrasts that vision to reality, which comes out decidedly… un-peachy.
POLLY AND MRS. PEACHUM. So that is all there is to it.
The world is poor, and man's a s***. (1.3.255-256)
It's blunt, and it rhymes. Polly and her mom sing about their vision of what life is like, and it's not such a ladylike lyric. Brecht uses upbeat rhythms and funny rhymes to convey really depressing ideas. The audience is beaten over the head with this one: poverty and inequality lead to violence.
MAC. One must live well to know what living is! (2.6.52)
While the Peachum family sing about how unfair and ugly life is, Mac is on the other side of the coin. All those violent lyrics from the Peachums are embodied in the figure of Mac, who sees things in a similar, dog-eat-dog way. Still, rather than complain, he decides to get while the getting's good and steal everything he can.
You lot, who preach restraint and watch your waist as well
Should learn for all time how the world is run:
However much you twist, whatever lies you tell
Food is the first thing. Morals follow on. (2.6.369-372)
"You lot" in this verse are the ones who have enough to eat and are therefore able to worry about portion control. The connection between morality and food goes both ways: you can apply morality to diet, but you can also see that those without enough food don't have much time to be holier than thou.
Mankind is kept alive by bestial acts. (2.6.380)
Leave your cute cat memes and inspirational quotes at the door when you go to see The Threepenny Opera; it's a bleak scene. A grim idea permeates the play: the world is a cruel place, and life is all about who can be the meanest to stay alive and on top.
For this bleak existence
Man is never sharp enough.
Hence his weak resistance
To its tricks and bluff. (2.7.182-185)
See the ABAB rhyme scheme? That fun, sing-song quality contrasts pretty starkly with the serious and un-fun message of the song. The lamentation, that humankind is not made for the ugly world we're born into, would be more expected in a slow dirge. The unexpected contrast makes audiences sit up and take notice.
Since this is opera, not life, you'll see
Justice give way before humanity. (3.337-338)
Let's unpack these little, snarky lines. The characters are singing about how, because they're in an opera, justice will be served. That means that, in real life, justice doesn't win out—humanity does. And if humanity is in opposition to justice, and usually wins in life, that means things are really unfair in the human world.
MRS. PEACHUM. So it all turned out nicely in the end. How nice and easy everything would be if you could always reckon with saviours on horseback. (3.9.360-362)
The snarkfest continues. Mrs. Peachum is commenting on the deus ex machina, the horseman who comes in at the last minute to save the day, sort of winking at the audience to saying that, obviously, the play is not reflecting real life. Such luck never happens there.
Injustice should be spared from prosecution:
Soon it will freeze to death, for it is cold.
Think of the blizzards and the black confusion
Which in this vale of tears we must behold. (3.9.371-374)
Mysterious, eh? Let's see what we can do with this metaphor. So the song, which we've already seen is pretty ironic, is saying that injustice should not be prosecuted because it's so cold it's freezing to death anyway. Great, so injustice is cold. The blizzards in the next line that we have to deal with, then, are injustices. And the vale of tears? That's a biblical phrase that means earthly life.