For others, supersize deals appealed.

“You work so hard, you want to use your money in a smart way,” said Aris Ramirez, a community health worker in Brownsville, explaining the thinking. “So when they hear ‘twice the fries for an extra 49 cents,’ people think, ‘That’s economical.’ ”

For Ms. Angeles, the excitement of big food eventually wore off, and the frantic pace of the modern American workplace took over. She found herself eating hamburgers more because they were convenient and she was busy in her 78-hour-a-week job as a housekeeper. What is more, she lost control over her daughter’s diet because, as a single mother, she was rarely with her at mealtimes.

Robert O. Valdez, a professor of family and community medicine and economics at the University of New Mexico, said, “All the things we tell people to do from a clinical perspective today — a lot of fiber and less meat — were exactly the lifestyle habits that immigrants were normally keeping.”

As early as the 1970s, researchers found that immigrants lived several years longer than American-born whites even though they tended to have less education and lower income, factors usually associated with worse health. That gap has grown since 1980. Less clear, however, was what happened to immigrants and their American-born offspring after a lifetime in the United States.

Evidence is mounting that the second generation does worse. Elizabeth Arias, a demographer at the National Center for Health Statistics, has made exploratory estimates based on data from 2007 to 2009, which show that Hispanic immigrants live 2.9 years longer than American-born Hispanics. The finding, which has not yet been published, is similar to those in earlier studies.

Still, the data does not break down by generation. Ms. Arias cautioned that subsequent generations — for example, grandchildren and great-grandchildren — may indeed improve as they rise in socioeconomic status, which in the United States is strongly correlated with better health.

Other research suggests that some of the difference has to do with variation among American-born Hispanics, most of whom still do better than the rest of the American population. Puerto Ricans born in the continental United States, for example, have some of the shortest life spans and even do worse than whites born in the United States, according to research by Professor Hummer, dragging down the numbers for American-born Hispanics. But Mexican immigrant men live about two years longer than Mexican-American men, according to the estimates by Ms. Arias.