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The assertion in bold from Eric Hobsbawm's The Age of Capital piqued my interest. I am quoting most of the paragraph in case the context may help.

A large part of the south-west – California, Arizona, Utah and parts
of Colorado and New Mexico – were ceded by Mexico after a disastrous
war in 1848–53. Russia sold Alaska in 1867: these and older western
territories were transformed into states of the Union as and when they
became economically sufficiently interesting or accessible: California
in 1850, Oregon in 1859, Nevada in 1864, while in the Middle West
Minnesota, Kansas, Wisconsin and Nebraska acquired statehood between
1858 and 1867. Beyond this American territorial ambitions did not go
at this point, though the slave states of the South hankered after
an extension of slave society to the large islands of the Caribbean
and expressed even wider Latin-American ambitions. The basic pattern
of American domination was that of indirect control, since no foreign
power appeared as an effective direct challenger: weak but nominally
independent governments which knew that they had to keep on the right
side of the northern giant.

To what exactly might Hobsbawm be referring? Is there evidence to support this statement?

Yes, the South was closely linked to the U.S. imperialist project in Latin America. Not only did slave states hope to gain advantage in Congress, they firmly upheld a pre-Enlightenment, neo-feudal model of race in which native Americans and mixed-ethnicity Latin Americans were subordinate to Nordics and Anglos. The issue of U.S. southwards expansion spearheaded by Southeners was in evidence long before the period Hobsbawn described.

According to William Carrigan's Forgotten dead: mob violence against Mexicans in the United States, 1848-1928, white settlers arrived in the Latinized West maintaining the traditional anti-Spanish Black Legend. Their disdain for Latino people was obvious: Carey McWilliams recorded one King Fisher who counted kills by notches on his gun: "37, not counting Mexicans." This racism was harnessed to Manifest Destiny and the result was expansion into previously Hispanized lands.

The trend may have began with Andrew Jackson, from the Carolinas. He committed the incursion that resulted in the 1819 Adams-Onís treaty in which the U.S. obtained Florida from Spain. In the 1830s southern settlers in Texas were successful in separating it from Mexico, as they were in attaching it to the United States a decade later.

After failing to purchase California and New Mexico for cash, the U.S. obtained them by invading Mexico. This war was principally supported by Southerners and resisted by Northerners. Henry Thoreau and Ralph Waldo Emerson, both of Massachusetts, vocally opposed it. According to Levinson's Wars within War: Mexican Guerrillas, Domestic Elites, and the United States of America, 1846-1848, at the time of the invasion the U.S. debated several options including conquering all of Mexico or only the part down to the 26th parallel. The challenge of integrating millions of dark-skinned Spanish speakers appeared too great for the U.S. to take the more ambitious options. California's statehood process was then controversial because of the question of whether it would become a slave state.

Future expansions became more nebulous, or at least less agreed upon. Filibusterers, especially William Walker of Tennessee, sought to seize more land in Mexico and Central America for slave interests. More proposals to seize parts of Central America and the Caribbean, such as John Slidell of Louisiana's attempt to acquire and integrate Cuba, continued through the 19th century even after the U.S. legally abolished slavery.

Later, the questionable labor practices of the United Fruit Company, headquarted in New Orleans, triggered extensive violence in several countries in Central and South America. Its close and corrupt relationships with weak client states was the origin of the term "banana republic". Rather than allow Latin American peoples to dilute white domination within the United States, the peripheral countries were by then controlled mostly at arm's length.