Depends on which weeds are growing. If they are just annuals, then covering them with either a thick mulch of compostable material, or covering them with something which keeps the light out, will be fine, unless they've seeded everywhere, in which case they will all pop up as soon as you start watering in the spring. Be careful which kind of carpets you use - they need to be wool. Synthetics don't break down, but do disintegrate on your soil.
If the weeds are perennials such as couch grass, great bindweed, mare's tail, creeping thistle, nettles, buttercup and so on, you have no real choice but to dig them out, or to use weedkiller if you want to poison your soil.
The better you clean up before you start planting, the less weeding you will need to do later, but remember that weeds love the growing conditions in a polytunnel just as much as plants do, and they seem to get a headstart.