I was walking in the area and one of the neighbors is using some heavy flexible black plastic matting with ribs as a Weed Blocker.
I asked about the material, he said he got it at a local building supply.
I use local building suppliers, so I looked around, nothing similar on display nor did anyone know of it... funny.
I haven't seen this neighbor since so I can't verify WHAT Local Building Supply Store he was referencing, but I need to visit him because this stuff was HD, thick and it looked like it would do the trick for water run off areas too.
As to using Round-Up... not too sure of it with all the controversy, I use Brush-Be-Gone, by Ortho, good stuff, (not sure if I will be dead from using it) but in New England it was one of the only products that would kill the woody stemmed Poison Ivy. Just to point out I only use it once a year, a lot of wells in the area even though I don't think it will get that deep, but the wife seems to think so and she lets me know every time I even think about using it !