There’s a fairly brief description of how Berliner Weisse was brewed in a book published in 1842.
Berliner Weisse was brewed from 5 parts wheat malt to one part barley malt.
The malt was mashed in with water at 35º C, 35.35 litres per 55 kg of malt. Another 80 litres of boiling water were added to the mash and mixed in.
Some of the thin mash was transferred to the kettle and brought to a boil with 0.234 kg of Altmark hops per 55 kg of malt. The hops had been soaked in water or very thin mash for 30 minutes beforehand.
The boiled mash was returned to the mash tun, raising the temperature to 72.5º C. The mash was left to stand for 30 minutes, then pumped to the cooler.
45.8 to 57.25 litres per 66 kg of malt of boiling water were poured over the goods in the mash tun to form the second wort. This was mixed with the first wort and when, the temperature had fallen to 18.75º C, yeast was pitched. The next day the beer was already delivered to pubs.
The author makes this interesting comment about wheat beers in general:
"all wheat beers, especially in the summer, easily turn sour and sometimes even sour during the brewing process."
And, finally, there’s a mention of smoke. Zimmermann recommends that those still using an old-fashioned smoke kiln should use dry oak, beech or coke as fuel, as these gave off relatively little smoke.