The Balfour Declaration was a document issued by the British government, not a statement by Zionist leaders. The initial draft of the declaration, which was drafted by Chaim Weizmann and other Zionists, did not make any mention of the rights of the Arab population of Palestine. Here's their draft, which they submitted to the British government:

His Majesty's Government, after considering the aims of the Zionist Organization, accepts the principle of recognizing Palestine as the National Home of the Jewish people and the right of the Jewish people to build up its national life in Palestine under a protection to be established at the conclusion of peace following upon the successful issue of the War.

His Majesty's Government regards as essential for the realization of this principle the grant of internal autonomy to the Jewish nationality in Palestine, freedom of immigration for Jews, and the establishment of a Jewish National Colonizing Corporation for the resettlement and economic development of the country.

The conditions and forms of the internal autonomy and a Charter for the Jewish National Colonizing Corporation should, in the view of His Majesty's Government, be elaborated in detail and determined with the representatives of the Zionist Organization.

The British government felt that it could not issue a statement that made no mention of the rights of the original inhabitants of Palestine. It also watered down the language about "recognizing Palestine as the National Home of the Jewish people," instead saying that it favored "a national home for the Jewish people" in Palestine. Note the important difference between those two wordings.

Ben Gurion's letter to his son is fairly clear. He describes in some detail that his goal is to eventually take over all of Palestine. His son complained that the Peel Commission had recommended only a small Jewish state in Palestine. Ben Gurion replies to his son that in politics, you can't let feelings of personal insult get in the way of practical measures. A small Jewish state in Palestine would be better than no Jewish state, and that state would be able to expand. Ben Gurion's writes that once a state is established, it can begin bringing in the diaspora ("exiles"), and building up its economic and military strength. He writes that the Jewish state can purchase land from the Arab states and offer them inducements, but that if they don't give up land willingly, then the Jewish state can speak to them in a different language (meaning force). He gives the example of the Negev. He says that the Arabs are not using the Negev to its full potential, but that they still might be unwilling to part with it. He says that it is moral for the Jewish state to take the Negev by force is there is no other way, because the Jewish people need it and the Arabs aren't really using it.

He's making an explicitly expansionist argument, justifying military conquest if more land cannot be purchased.