In Chapter 22 of To Kill a Mockingbird, what does Atticus mean when he says, "seems that only children weep"?

On a literal level, the line refers to the fact that it seems like only the children (mostly his children) were surprised or emotionally moved by the trial's verdict. They are still innocent, and so can still be hurt by the world's injustices. Adults, on the other hand, are armored and cynical, and so don't cry just because something bad happens. Now, there are two more ambitious ways this can be read. One is within the book, linking the line to the novel's epigraph. To be a lawyer is to put aside one's childhood heart: to armor up.

More generally, Jesus spoke of becoming like a child again, and that sort of open-hearted compassion would be familiar to the citizens of Maycomb from their churches.