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.
He gave his second son August (Heinrich's father) not only the duchy of Saxe-Weissenfels, but guaranteed to him and his heirs the possession of the county of Barby in the event of the extinction of the count's line.
The title brought him prestige, but neither a seat nor a voice in the Reichstag, nor sovereignty within the duchy of Saxe-Weissenfels, rather political dependence on the main line of the family and the Electorate of Saxony.
Following the example of his cousin Johann Georg, Duke of Saxe-Weissenfels, he created in 1699 a Citizens' Company (Bürgerkompanie) with the responsibility of ensuring order during civic celebrations.
Elisabeth's paternal great-great grandmother was Countess Agnes of Barby-Mühlingen (1540-1569); this give to Heinrich some blood ties to the extinct House of Barby.