The Beggar's Rags, fluttering in Air, Does to Rags the Heavens tear.
The beggar's rags tear the heavens into rags in the same way that "the robin redbreast in a cage" puts "heaven in a rage." Little things contain bigger things—the devil is in the details. It's the "world in a grain of sand" all over again.
In this case, a small example of poverty and suffering tears apart the sky itself. All of reality is taking part in the beggar's suffering, just like with the robin at the beginning.
The Soldier arm'd with Sword & Gun, Palsied strikes the Summer's Sun.
Blake was opposed to the British Empire—he didn't think that Britain had any business in controlling other countries. In fact, he supported the American Revolution for that reason. So, he has a bee in his bonnet about the military.
It's not that Blake thinks soldiers are bad people (though he did have a run in once with a drunken soldier, who later accused Blake of treason), it's more that he views the soldier in this couplet as the pawn of other forces.
Even though the soldier is armed with a sword and a gun, he's "palsied"—meaning paralyzed or afflicted with uncontrollable movements. This probably means that the soldier doesn't have any free will. He's the servant of those commanding him, of the people who are in charge of the Empire.
In this state of paralysis, the soldier's striking the sun—a pretty big target (and another "world in a grain of sand" moment). Blake's probably suggesting that what the Empire is doing is a similarly blasphemous trespass against the nature of reality: if you strike the sun, you might damage the light that warms the entire globe.