Depends how deep you are able to put it, either way if you can get cardboard & put that down it will help exclude the light, then a good 6 inches of well rotted manure. Only perennial weeds should be able to penetrate that & then in a weakened state, so you can just trowel them out.
Voila you will have created your first no dig bed, with minimum work, as you were going to apply manure any way