It depends on the types of weeds you have. If they are perennial then they will grown straight through. Annuals should be ok if you use a thick layer.
We use woodchips, but have a good 3 inch layer which we keep topped up. No annual weeds. We did get the off bits of bindweed coming through at first, but I zapped them by painting on glyphosphate and that has finished them off. This area was very weedy before, but we did clear by pulling out all the roots and digging a number of times.