My husband and I just put down the black liner this year and so far so good. Keep a thick layer of mulch and it’s not noticeable.

Black liners, plastic or fabric, do NOTHING to keep down weeds, which grow from seeds on top of the liner (and through it). In addition, once it begins to degrade, removal is a nightmare. It's the mulch the previous poster mentioned that's keeping her weeds down. The liner is irrelevant.

Round up.

Trim the weeds BEFORE they form seed heads.

If you live in an area blessed (cursed) with good soil, you'll probably need most/all of the solutions posted above: weed barrier cloth, annual mulch application, diligent weeding, and chemical weed-killers including pre-emergents and glyphosate. OR, you could try using dense, low sedum. It might inhibit some of the other weeds, but it also might crawl into the creek bed and give you a new problem. I'm beginning to think the weeds always win in the end.