According to this address, why should the United States expand overseas?
What benefits would expansion bring to the United States? What benefits would the United States bring to its annexed territories?
Beveridge's primary claim of expansion lies in his zealous support of Manifest Destiny. Asserting that expansion and imperialism were in accordance to divine providence, Beveridge was completely convinced that it would be an economic and political boon to continue the expansion of the United States into the Philippines and beyond into the Pacific Rim. Beyond this Beveridge advocates the idea that the United States influence of "civilization" justifies expansion. As consistent with the time period, there is a Social Darwinist argument present in that if the United States can do it, it should proceed with being able to exercise its military might in establishing itself abroad. The swooning rhetoric in the address helps to convince the readers that Beveridge not only envisioned a political program where the United States ascends to the world stage of power, but also a platform to advance his own ambitions.
I would say that there are three main reasons in Beveridge's mind.
The first is the idea of the "white man's burden." Beveridge believes that Americans have a duty to spread their religion and their government and culture across the world. This will help the people upon whom the US imposes its rule. They may not like it (like children don't like being ruled by their parents) but it is good for them.
Second, the US will get commercial benefits. He talks about how big Cuba and Hawaii and the Philippines are and how they can help us get rich.
Finally, he says expansion will make us more powerful. He talks about bases in Hawaii, in the Marianas (he calls them the Ladrones), and in the Philippines -- these would extend the reach of our navy in a major way.