Northern Mexico contained few of its people for much of its history, if the U.S. decides to annex everything North of Tampico, as late as 1900 fewer than 15% of Mexico's population lived in that region. In 1848 that population was less than 800,000, a large number of whom were indigenous peoples with whom the Spanish and later Mexican governments had a small degree of formal control over until the 20th century. The states in the North did receive a large number of migrants from central Mexico, and at least according to the Mexican Census' around one in every four inhabitants in the region was born elsewhere by 1970. In Baja, that number was even higher, with half of the inhabitants being born elsewhere.
Northern Mexico also contains much of the country's irrigated agricultural lands, producing around 35% of the country's annual agricultural output, including nearly 90% of the country's cotton production. The Mexican heartland by contrast produces most of its corn, beans, livestock and what one traditionally associates with "Mexican cuisine". It also contains around one-third of the natural gas production, but very little of the country's oil.
The Southern Region of Yucatan, and Quintana Roo remained heavily indigenous and underdeveloped until the arrival of tourism in the late 20th century, with Campeche being more Mexican in character, but containing fewer people. Around 3% of Mexico's population lived there in 1900. As late as 1940, around 40% of the population consisted of monolingual speakers of indigenous languages. The area did become important for the production of henequin and produced some sugarcane as well. I imagine the U.S. rule over this area would be much more colonial in nature, with few Americans settling the area, at least for the first century. On the other hand, I can also envision a scenario where the U.S. takes advantage of separatism in Chiapas to annex that state along with Tabasco later on to have a transcontinental territory, or at the very least to establish an independent republic under U.S. aegis.