hate to be the one to say it, but that black plastic is BAAAAD stuff! it kills your soil - the microorganisms can't survive with that cover. you want somethign that will eventually be able to break down the soil underneath as well as your upper soil that you bring in
if you're going to put it down, you need to pull it up and let the soil "breathe" for a couple of weeks again
BG is absolutely right!

On re-reading my explanation wasn't clear - you don't leave the plastic there forever - just a week (or two at the most) as that is all it takes to cook the weeds. BG is wise...