What does it mean “Hang the boy”?
It reminds me “hang up”.
At a guess, I’d say it’s a mild form of cursing like “drat the boy”, meaning “oh, what has he done now?” It’s a long time since I’ve read the book, so it could also mean what it says “Hang him!”, but that would appear rather cruel.
It is pretty much the equivalent of “damn it!”
Literally, it means to hang him for his inadequacies.
If you are unfamiliar with hanging, here is an article.
Just remember, it’s a figure of speech. She doesn’t really want to hang him. 
Edit: Crud! I type to slow. Ninja’d by Sanne!
Edit edit: to = too
LingQ is in desperate need of an edit button. 
@ Xakota: how do you know it didn’t take me hours to type the comment?
It may be a short form of “let him go hang (for all I care)”. In other words, he can get into as much trouble as he chooses, even to the point of being hanged by the authorities, and I will do nothing to help him. Again, not to be taken literally. Although in those days they probably did hang boys for fairly minor crimes.
Not like today, eh 
Sanne: I don’t. But you posted before me. So who is the slowest? Me, I say. 
Thank you for everybody. I thought it had other meaning.