I believe that Fitzgerald does this to reinforce or introduce one of the main themes of the novel. One of the major things that this novel is about is the American dream. It is about people and their hopes and dreams of getting ahead.
The character of Gatsby is said to be representative of the American dream. He is a man who is self-made, who has built himself up really without any help.
Because this is a major theme in the book, it makes sense that the author would use those words a lot to get the idea of hopes and dreams into the reader's mind.
Concerning Fitzgerald's use of the words hope and dream in The Great Gatsby, one should be careful about trying to speak for the writer. No one can say why Fitzgerald does anything in his novel. We can only speak about the functions and results of what he does. Communication is far too complex for you or me or anyone else to speak for the writer.
That said, the words hope and dream do reveal the idea of the American Dream. In addition to that, they reveal one of the aspects that make the novel beautiful: Gatsby's love for Daisy. His foolishness and naivete do not cancel out his dedication to Daisy and his capacity for hope. This, after all, is what Nick likes so much about Gatsby:
...[Gatsby's] extraordinary gift for hope, a romantic readiness such as I have never found in any other person and which it is not likely I shall ever find again.
There's an early usage of one of your key words for you.
Fitzgerald upholds the American dream in his novels and short stories so its fitting that the words dream and hope act as motifs that repeat throughout the novel. Gatsby himself represents the American dream since he is a typical rags to riches success story.
Fitzgerald's book mirrors the headiness, ambition, despair, and disillusionment of America in the 1920s: its ideals lost behind the trappings of class and material success.