"sweet names"

I lived close to a Puerto Rican family in Indiana, in the late 1970s, who used these terms of endearment, so it is not recent and must be wide spread through the latino culture.

It is certainly common practice in New York City for store clerks to use it with their regulars. I've only heard it used in addressing adults. I think that the clerk's not knowing the name of the customer — or having too many names to recall — contributes to its ubiquity.

Several people in my wife's family, who are of Mexican descent, call their children "mamasita" and "papasito."   It often gets shortened to "mama" and "papa."   I hear it more and more, but I can't say when it started, since my exposure to the culture prior to the last two decades was limited.

It seems to be used more when the child is an infant or toddler, and used less as the child ages.   I've found with my children that as they start to respond to their own names, I call them more by their own names and less by nicknames or other terms of endearment.   The "mama" and "papa" terms seem to follow the same pattern.

Very much as Anglo children (at least north of the Mason-Dixon line) grow up calling their parents "Mommy" and "Daddy", and graduate to "Mom" and "Dad" at some point—at about the same point, in fact, that their parents switch from calling him "Bobby" to "Bob", and at which birthday cards addressed to him switch from "Master Robert Bridges" to "Mister Robert Bridges".   In the Southeast, it's much more common for adults to go on calling themselves "Bobby" and their fathers as "Daddy".   I don't recall "Mommy" continuing into adulthood even in the South.

Strictly as a nitpick, I don't believe "mamasita" is shortened to "mama"; rather "mama" is the base form and "mamasita" is the expanded affectionate version, as "Juanito" is the affectionate or diminutive form of "Juan".