Stanza 3 Summary

Lines 9-10

How the Chimney-sweeper's cry
Every blackning Church appalls;

• Things start to get just a wee bit trickier in the poem's third stanza. Don't worry, we said "wee bit," and we meant "wee bit."
• The key here is that you have to pretend the word "hear" is still floating around somewhere. In other words, the speaker also "hears" how the chimney-sweeper's cry "appals" "every blackning Church."
• Yes, "appalls" is the verb that goes with "chimney-sweeper's cry." It's weird that it occurs at the end of the line, but that's okay. This is poetry.
• A chimney sweeper, or a chimney sweep, is, or was, exactly that: somebody that cleans chimneys. Back in Blake's day, this wonderful, disgusting, dirty, dangerous job was usually reserved for children, as you can read about here. 
• Did we say kids? Yes, kids, usually really young ones. These little kids went down the chimneys to clean them because they were small enough to fit, and hence ideal for the task. You see, there weren't really any child labor laws, more like none whatsoever. While eventually kids received protection from this sanctioned abuse (there's really no other way to describe it), it lasted long enough. Chimney sweeping was a really dangerous job. Most of the kids that were lucky enough to do the work were orphans (often under the protection of the church), and they usually didn't bathe very often and were thus dirty for days on end.
• Besides being really icky, soot, as you may have guessed, is also very carcinogenic. Lots of kids got lots of cancer from spending so much time working in it.
• Also, the risk of going down a chimney to clean it, Santa Claus style, and then getting stuck was totally real, if not common, or always likely. So, just add this to the whole cancer thing.
• Anyway, as we mentioned, this job usually fell to orphans in the care of the church and other religious institutions, which explains why the speaker mentions a "blackning Church."
• Speaking of that church, let's make sure we're on the same page with that word "blackning." That word just means "blackening," but it's not clear if the church is becoming blacker (i.e., in a state of blackening) or blackening other things (like little kids).
• Come to think of it, they're both kind of the same thing. The church, which was partly responsible for this whole chimney sweeping business, was responsible for "blackening" those little kids.
• It made them both literally blacker (they were covered in soot) but also metaphorically blacker, in the sense of less innocent and closer to death (death is often associated in poetry and elsewhere with the color black).
• Because the church is involved in this deplorable practice, it, as an institution, is becoming blacker—less good, pure, and devoted to the betterment of humanity.
• All of this brings us back to that strange word "appalls." We'll admit, it's a funny word to use here—and not funny as in hilarious, but funny as in strange. It seems to have the sense of "shames" or "casts aspersion on," or something like that. The chimney sweepers cry, the church is partly responsible for it, therefore that cry shames the church.
• Note: it is possible that the church is appalled by the cries, in the sense of shocked, but this seems less likely, given the church's historical ties to the practice. 
• And we wouldn't be doing our job if we didn't tell you that Blake was really, really against child labor. Side note: is anybody actually pro child labor (aside from The Simpsons' Mr. Burns, that is)?
• Anyway, chimney sweeping was one of Blake's go-to points of attack when it came to the whole child labor business, but also, as we see here, when it came to attacking his own historical moment. This chimney sweeping stuff irritated him so much that he wrote two poems about it, one each in the Songs of Innocence and the Songs of Experience. You can read about those poems right here and here. 
• As for just what exactly these lines mean, well, get your metaphor caps on because the speaker is leaving the literal behind.
• Obviously, a chimney-sweeper's "cry" can't really do anything physical to a church, so we'll have to come up with some other kind of explanation.

Lines 11-12

And the hapless Soldier's sigh
Runs in blood down Palace walls.

• If you're expecting to have to carry that word "hear" again you can relax. Here, the speaker simply states a fact, as a sort of addendum to his little bit about the chimney sweeping stuff.
• Now he tells us that there's a "hapless" (i.e., unfortunate) soldier, whose "sigh / Runs in blood down Palace walls." Well, cool.
• We didn't know sighs could actually run down walls in the form of blood.
• You didn't know that because it doesn't really happen. This is all part of a gnarly metaphor.
• The basic idea is that the Palace, which is here a symbol for government, royalty, etc., has blood on its hands, so to speak.
• Okay, but what are we to do with these bizarre lines? Think of it like this. First, the soldier sighs about something (his recent wartime experiences, his government's military policy, etc.).
• This sigh, an exhalation of breath, is the expression of whatever is bothering or upsetting the soldier. And we know that, because he's "hapless," he's helpless to do anything about what's bothering him—except, you know, sigh in blood.
• The sigh runs in blood because, well, it has to do with the palace—i.e. the government that dictates policy in the first place.
• It's like the soldier exhales, an ineffectual, "hapless" gesture that shows how powerless he is to change his situation. Instead, all he can do is defend the all-powerful Palace, or (worse) enforce its orders with violence (after all, soldiers tend to be trained to do that sort of thing). 
• And so, the expression of both his discontent and powerlessness (the sigh) turns to blood and runs down the palace walls. The Palace is marked by the bloodshed that the solider would be forced to carry out. This image, then, is another reminder of the "manacles" the speaker mentions in line 8. He says that these restrictions are everywhere, but now in this stanza he's giving us two examples to prove his point: the suffering chimney sweep and the solider—who as a tool of the "Palace" (or government), is powerless to prevent himself from causing the suffering ("blood") of others.