Who say this in The Road and what does it mean?
"Do you think that your fathers are watching? That they weigh you in their ledgerbook? Against what? There is no book and your fathers are dead in the ground."
This passage is really fairly obscure. The meaning itself is rather easy to determine, but the context of the meaning cannot be determined from within the passage. In addition, there is some legitimate ambiguity about who the speaker actually is.
Part of the post-modernist fragmentation of identity is developed through unidentified speech in dialogues. There is no "he said" "he replied" etc. Dialogue is only indicated by margin and indent set-off in the typography.
Before the quote you ask about, the boy is asleep. The father goes to look out on the road. He sees a group of four people gathering at the top of the road in the distance. He watches them advance, fearful they will choose to stop there. He watches them pass on by.
He goes back to the campsite to be with the boy. He gets his map with "limp and rotting pages." Now he starts talking. We are told that the boy is still sleeping:
they wrapped themselves in their blankets and took turns watching but after a while the boy was asleep.
When he sits down with the map, he talks to himself. Though he says "we"--"You always think we've gone further than we have"--he is talking to himself because the only ones are he and the boy, no one else.
Then we're thrown a curve (as in a baseball allusion) in the line before the quote you ask about. Suddenly we are told: "They sat looking out through the trees at the road." Who is "they"? From this text passage, we cannot say who "they" is; we don't know.
The quote itself seems to be spoken by the father. There is some doubt here though because the margining of the lines is spread out more. Does this indicate an entity in his consciousness that is engaging in the conversation--a spiritual connection to an Other? Or does this indicate simply that he is in his Super Ego and scolding himself for the beliefs or thoughts he holds in his Ego. At this point in the narrative and in relation to this bit of text, it is impossible to definitively say who is speaking here:
"Do you think your fathers are watching? ... your fathers are dead in the ground."
We can make a logical assumption about who is speaking, though (and, really, there is logic to support either side). Based on the text in this passage, it is most logical to think that the father is still talking to himself and that his Super Ego is scolding his Ego. Either way, the text suggests the voice is an interior voice in the father's mind, so, metaphysics aside, the baseline answer is that the father is the essential speaker (the debate is whether he is, himself, scolding himself or some spiritual Other in him is scolding him).
Whichever the case may be, what the passage means is that the speaker is questioning moral integrity and conscientiousness because there is no one around, there are no spirits, no ancestors watching over them; there is no spiritual Other who records his moral and ethical choices to determine if he is worthy or unworthy.
The sum of what is being said in this quote is that he is all alone in the vast empty universe--a wider desolation than the vast empty planet--and no one hears him; no one sees him; no is concerned with or about him. He is desolate. He is alone. He and the boy, who is his only companion--and yet who is his charge and obligation--are totally completely alone in the midst of strangers and monsters in the form of humans.