What do you mean by "barrier rolls"? Is that a landscape fabric and if so what kind. There are some that have very fine mesh that all sunlight would be blocked and there are others woven so loosely that they block no sunlight.

How much mulch was placed on top of the "barrier"?

Weed blocker mulches will help control unwanted plant growth, aka "weeds", but will not totally eliminate it, and some of those unwanted plants are strong enough that little will stop them except continuous cutting of top growth so eventually the roots are starved of the nutrients the need to keep growing.

What do you mean by "industrial weed killer"? What is available to you as an average consumer is usually sufficient to control most unwanted plant growth, but for the really powerful, aka industrial, poison you need to be a Licensed Applicator.

kimmq is kimmsr

Keep in mind that seeds can fall on top of mulch & sprout too...