How long did you leave the weed suppressing fabric on Calvadnack? I've noticed that TV presenters make claims such as 'leave it on for a few months and your problem's gone'. My experience is different, especially with tough weeds such as couch grass, creeping thistle etc, and I suspect it applies to silverweed too. I have found that even after a year these weeds have not been killed. The top growth may be gone, but the instant they get some light they're off again. In particular, when you use a fabric with growing holes in, the weeds get enough light to pop up along with the veg. I think to exclude all light, you need a thick mulch of strawy manure, with the fabric over it, then more old straw, about a foot deep, on the top. Big thick cardboard boxes opened out under that lot will help with the light exclusion. For the first 12 months at least, grow nothing through the fabric, then in the second year, try making holes through it. I have a feeling though that once you have a really rampant weed you will need to cover your ground with a thick mulch forever
Where the weed has runners, they will pop out through the sides and get the light for the whole plant that way. Couch can pierce a hole through a potato, which shows how determined these plants can be.