If the cover is left on for a few years it will kill the grass and small annual weeds. Any strong rooted perenial weeds like dandilions, docken or couch grass will just sit and wait until you remopve the cover.

I did this on a new allotment with couch grass, rosebay willowherb etc. I used the stuff farmers wrap haylage in.Left down for a year and it worked like a charm. Any remaining toughies were easily dug out but there weren't many. But it isn't pretty!

PS But can't remember if all the couch disappeared - it was an old meadow and it invaded from everywhere. But there was certainly a lot less of everything.