Heinrich's grandfather, the Elector Johann Georg I, who was also a feudal lord of the county of Barby, chose to make land provisions in his will for his three younger sons.
When August Ludwig, the last count of Barby-Mühlingen, died childless in 1659, some parts of the county were inherited, in accordance with Johann Georg I's will, by Heinrich's father August of Saxe-Weissenfels, who in consequence became count of Barby.