for the many centuries when you couldn’t be confident that your water supply wouldn’t kill you, small beer was the thing to drink to quench your thirst, for adults and children alike. My grandfather was given small beer at his school for that reason in the 1880s.
The idea that Medieval people drank beer or wine to avoid drinking bad water is so established that even some very serious scholars see no reason to document or defend it; they simply repeat it as a settled truth. In fact, if no one ever documents the idea, it is for a very simple reason: it’s not true.
(the American food history blogger Jim Chevallier disses what he calls The Great Medieval Water Myth.)
On the subject of Shakespeare and beer, as I may have mentioned here before, he was writing at a time when ale (still unhopped) and beer (the hopped drink brought over from the Continent) remained separate drinks. You could make small beer because the hops would preserve it, but “small ale” would soon turn sour. Beer was an urban drink, ale maintained its popularity in more rural districts – even in 1630 the pamphleteer John Grove wrote: “The City calls for Beer … But Ale, bonny Ale, like a lord of the soil, in the Country shall domineer” – and Shakespeare apparently kept a Warwickshire love for ale even after he moved to London, since in his plays every mention of beer is disparaging, and every mention of ale involves praise, from “blessing of your heart, you brew good ale” to “a quart of ale is a dish for a king”.