Thanks.
Interesting that the English Wikipedia on Barby reads a little differently, and does not mention any change in territory, just a change of ruling house:
Since the 12th century, the area was enfeoffed to the Counts of Barby descending from nearby Arnstein, who achieved Imperial immediacy in 1497. Upon the extinction of the line in 1659, the County of Barby fell to the Duchy of Saxe-Weissenfels, ruled by a cadet branch of the electoral Saxon House of Wettin.
But maybe something was lost in translation.
Let's see what others say including @escoins (meanwhile, I will set up these two rulers attached to Barby, and we can change later if the consensus is to set up the issuer Saxe-Barby).