The Company, Weyland-Yutani, does not have their own marine force. The marine force in Aliens is the United States Colonial Marine Corps, a force the United Americas deploy to its colonies when there's insurrection or trouble. When the colony Hadley's Hope on LV-426 went dark, the Colonial Marines were deployed along with representatives from the Company who ran the colony.
At the time of Alien and Aliens, North America, Central America and South America have merged into a union called the United Americas. It doesn't seem to be a country, but a union of sovereign states (more akin to today's European Union), where the most powerful one seems to be the United States because of their position as a starfaring, colonizing power, and they also control the United States Colonial Marine Corps. It seems like the Three World Empire, consisting of Japan and the UK (in which Weyland-Yutani, a merger of a British and a Japanese company, have significant pull) and several developing countries, are allied with the United Americas somehow, although this has not been fleshed out.
This information comes from the Xenopedia and this blog entry, which cites auxiliary canon sources like the Aliens: Colonial Marines Technical Manual and easter eggs on the Alien Anthology DVD box set. It's not spelled out in the movies.