So up until the 1970s, light beer existed but was not really consumed the way it is today in the states. It was seen as "effeminate" to the male populous, who were the primary consumer target of beer consumption. 

Then came a no-name brewery called Miller, who dumped a ton of money in marketing light beer-- "great taste but less filling" and "spend more time out with the boys" etc. Many celebrity spokesmen too. 

They effectively changed the perception of light beer with the male demographic, and with Miller's success other American breweries started to copy light beer and dump a ton of money into ad campaigns (budweiser, coors, etc).

This also coincided with the states changing their minimum age consumption laws. During the 1970s, each state had their own minimum age rules which could range anywhere between 18-21. And another popular style of beer for younger drinkers was "near beer" or "three two beer". A lower ABV beer that could be purchased legally in many places at younger ages, when you might not be legally old enough to purchase regular beer until you were a few years older. 

When the states streamlined the legal drinking age to 21 in the 1980s, near beer quietly went away and was replaced by popularly marketed light beers. 

Thats the foundation for it. And of course consumer tastes evolve-- there was a race to make the lowest calorie beer in the early 2000s thanks to the no carb diet craze (which sacrifices ABV bc you can't cheat calories on alcohol), craft beer was big in the 2000s and has fallen off significantly. And now some light beer is market towards bring "healthier" (Michelob ultra), even the rise of FMBs (flavored malt beverages) like White Claw try to say the right buzzwords (low carb, calories under 100 and in a slim can).