If birth control (actually discovered thanks to Mexican researchers) is still discovered in the 1960s as OTL but Mexican industrialization begins earlier, then Mexico may see either a later or more gradual decline in family sizes and population growth.
A lot of American stereotypes about Mexico and Hispanics are generally still imagine Mexico in 2018 as the poorer, '70s Mexico with 7 child families. Today Mexico has become much wealthier and the birth rate has hit 2 and change children per woman. Even if Mexico was still poorer, the demographic of young people willing to leave isn't there anymore.
If a family has 7 children on a farm (no matter what country) then 5 can leave and send money back home, but in a country of smaller families people generally stay put to take care of their parents or take over a family business. Outside of Africa, the Middle East, and parts of Asia, the two child family has become a global norm.
Population growth will be much lower in places like Bangladesh and Indonesia than in earlier decades, but there will be a youth bulge/demographic dividend where most of the population is working age adults. A more developed Mexico would face a Chinese style dilemma of whether it will get old first or rich first.
China's working age population peaked a couple years ago, but it may face Japanese proportions of retirees without Japanese levels of wealth to pay for pensions, etc. A more developed Mexico would become a destination for immigrants from other places, especially Central America.