Hi there!

I'll start by translating Burn's stat into something a little easier to work with. Per research by William Rorabaugh, Americans age 15+ around 1830 drank about 7 gallons of pure alcohol (as in, if you extracted the literal alcohol from the booze and added it all up) per capita per year. That's about 3.5 times what Americans consume per capita today, so yeah, that's a lot. An estimated 4.3 of those 7 gallons was consumed via distilled liquor (mostly whiskey by then but sometimes rum), plus another 2.7 via cider. Wine and beer were minor drinks then, lucky to get 0.1 gallons apiece.

Americans were drinking a ton, no doubt about it, but let's qualify before we get further: alcoholics skew the stats. Both then and today, the top 10% of drinkers consume much more than 10% of the total consumed alcohol. In turn, some adults don't drink at all. Unfortunately I don't have hard numbers for those proportions in 1830, but the point stands that not everyone drank equally.

These numbers were so high because whiskey and cider were incredibly available, incredibly cheap, incredibly alcoholic (cider was typically around 7-8%, though families occasionally refined it into an "apple jack" that was closer to 20%), and in part because Americans were drawing on English and Dutch drinking traditions that hadn't been built booze that strong. Americans drank at mealtimes, during work breaks, and right before bed, and the drinks kept getting stronger and stronger. Distilled liquors had steadily gained popularity since the early 1700s when the triangle slave trade brought cheap molasses up from the Caribbean. Over time it was displaced by whiskey made with cheap corn from western farms. Cider developed as cheap homemade product on farms: apple trees growing alongside farm fields and roads could provide multiple barrels per family per year without taking space from other crops. Tea was more expensive than both of these. Milk was harder to come by, plus growing children needed it more. Public water sources were often unhealthy at this point, and even when they weren't they were still perceived as unhealthy.

How did the US compare? It wasn't the best, but it wasn't the worst either. Around 1840 the US was consuming about 1.6x the alcohol per capita compared to the UK and Prussia, but Sweden was consuming about twice as much as the US, while France consumed 2.5x as much. If anyone knows why France was drinking so much, I'd love to know too!

Did American society just shrug this off? The (many) drinkers certainly did, but others didn't! There were two main drivers of opposition to alcohol: class (capitalism) and morality. Elites and employers didn't much care for drunk workers/publics, and moral reformers tended to believe they were saving the nation from itself (naturally, I'm generalizing for space here). Temperance societies formed in the 1810s and soon had millions of members, and elites had been enacting laws governing who could drink, when, how, and how much since the earliest foundation of the colonies. Whether they approached it from moral or economic perspectives, however, these folks believed that alcohol caused crime, disease, poverty, insanity, and many other social ills associated with an industrializing and urbanizing society.

The causes of Prohibition would be a long comment all on their own, but the 18th amendment was definitely not a direct intervention into this level of drinking. The temperance movement (plus economic and cultural shifts in the nation that facilitated a preference for beer) mitigated these levels of drinking long before that. By 1840 the US was down to 3 gallons of alcohol per capita (age 15+), and by 1845 it was down to 2. It's remained around that level ever since (and if you want to get picky, it was around 2.4 when Prohibition was enacted).

Source: William Rorabaugh's The Alcoholic Republic, probably still the best single work on early republic drinking patterns.