I'm confused on the link you provided, or perhaps I skim read it way to quickly. The article seems to say that that Jacob Black was born in 1801, and obviously couldn't have been Catherine's father, so I got lost in his connection to your Jacob. Isn't the article talking about a man who was in the Black Hawk War and was buried there in Illinois?
On what I can do for you is look into Jacob Black in Botetourt, and see what I can find. I've got some resources that may be helpful; we'll see. I'll post here what I find. My assumption is that he was born sometime before 1782, given that he was father of Catherine.