An American expat living in Amsterdam told me that real Heineken could only be found in the Netherlands. After the tanks were emptied, they would be rinsed out and this waste water was shipped to the US under the Heineken label. I've got nothing against Heineken here or in the Netherlands (Grolsch is better!), but the first time I saw a green tanker truck pull up to a pub on the Damstraat, attach a hose and pump in hundreds of litres of beer... let's just say the exotic import magic died a little.
There are similar jokes about Corona, but it's somewhat related to the real production of small beer. You make a strong, powerful beer, then add more water to the mash and brew a weak, inexpensive, low-alcohol beer with those leftovers. Similar to modern "light bitter" in England. If you're interested in detailed tables of official British beer classifications from the 1700s to the present day, someone else has taken care of that for you.
You don't see this style often, so when I first spotted a bottle of the Anchor Small Beer from San Francisco I had to try it. $3, 3.3% abv, 22 oz. bottle. It's pretty weak compared to a lot of the beer I've had recently. Very light in flavor and body, though there is a bitter finish that's nice. Gigantic soap-like bubbles. They died down after a while, but just look at the bottle and glass. I wouldn't mind this as a draft beer, particularly to go with lunch--not too heavy, not filling at all, and no need for a nap afterward.
My first exposure to the term was in literature, particularly from Victorian England. I don't have an exact quote here, but I recall multiple instances of children drinking it. The first time I saw "small beer" I thought it was a reference to the size of the glass or bottle, like a "small Coke". Later a helpful footnote explained the difference. And of course you often see it in the metaphorical sense of meaning trifling objects of no importance, similar to "small potatoes".
Some literary references:
It's mentioned in James Boswell's The Life of Samuel Johnson: an acquaintance named Foote tried to make money by partnering with a small beer brewer: "Fitzherbert was one who took his small-beer; but it was so bad that the servants resolved not to drink it."
Charles Dickens included it as part of the background details of the era in various works. From Little Dorrit: "He resumed this occupation when he was replete with beef, had sucked up all the gravy in the baking-dish with the flat of his knife, and had drawn liberally on a barrel of small beer in the scullery."
William Shakespeare made several references to it. In Othello, Iago details the duties of a woman including "To suckle fools and chronicle small beer", used here in the figurative sense to keep track of minor kitchen stuff. In Henry IV, Part 2, the future Henry V asks, "Doth it not show vilely in me to desire small beer?" as he's not quite ready to grow up. In Henry VI Part 2, right before the famous and oft-misunderstood desire to kill all the lawyers, Cade promises "I will make it felony to drink small beer". It should be noted that Shakespeare really loved unhopped ale made in England, and at the time hoppy beer from continental Europe was considered a separate beverage. Great to see that beer snobbery has a grand literary tradition.