Lewis Carroll is wildly funny. His works usually employ wry humor, often absurdist humor, occasionally over the top, broad "let's stuff the Dormouse' head into the teapot" humor.
"Where shall I begin?", is the question asked and many responses were possible from the king:
- I don't know, how long is it?
- Read the most relevant part,
...or even, simply,
- Just read the whole thing.
But the king says none of these. Instead, the king responds by stating the most mundane yet obvious thing possible: begin where? Well, you know, at the beginning. And then goes on to compound the obviousness: ...and then you go on. You know, like, to the end. And then compounds the absurdity further: ...oh, but then you stop. When you've reached the end. That's when you stop. The end.
The king has, before this point, said nothing but foolishness, and so here, just as before, instead of ever realizing that he was saying something mind numbingly obvious, speaks his response "gravely" ...as if answering a question of great gravity. As if this question were deep rather than as shallow as they come.
So. The word "gravely"? It's humour. Simple enough to be laughed at by a child, but enduring enough to last a few centuries thus far.