You can suffocate the grassy weeds by laying several thicknesses of newspaper over the areas between the beds. For a more permanent solution, carefully apply Round Up to the area. When the weeds are dead, cover the area with weed barrier landscape fabric. This will keep new weeds from sprouting. You can walk occasionally on the weed barrier - as long as you don't punch holes in it, it will effectively keep new weeds from sprouting.
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