Answer: Since you used black plastic and mulch in the beginning I would suspect any weeds are growing in the decomposed mulch rather than in the ground. Weeds can also take hold in the bits of organic matter that accumulate, along with moisture, on plastic under pebbles. In my experience junipers will eventually fill in and outcompete most weeds, but it can take a few years for this to happen. I am not a fan of plastic as mulch because it prevents air and moisture from reaching the roots, and can cause problems over time. Instead, I would suggest removing the plastic, trimming off the weeds as best you can and then sliding cardboard (recycled from corrugated boxes is ideal) in under the junipers to try to smother and exclude light from the weeds below. The cardboard will break down over time but is easier and faster to apply under the junipers than a heavy layer of mulch would be. Lastly, cover any exposed cardboard with mulch so it looks nice. If some persistent weeds manage to survive, you can try spot treating them with an herbicide containing glyphosate; follow the manufacturer's directions and be careful not to allow it to contact the junipers. Be sure to work on a calm day, go slowly and carefully and try using the wipe-on application method and an old trash can lid or similar material to shield the junipers from any drips or overdrift.
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