When one builds a sheet composting area of any size, an understanding of the reasons for each layer and how to maximize chances of success becomes important. A few thoughts in response to concerns/questions about this method; just one of many useful techniques for soil building:
Knock down/ mow the weeds- They will break down to add to nutrients. Persistent perennial weeds need to be dug and removed. Weed seeds are present in the ground whether or not one sees evidence of recent weed growth.
Spread a couple of inches of manure and any mineral supplements as a hot starter to the composting process and water it well before making the newspaper weed barrier. The newspaper does act as a weed barrier; it is also one of the carbon elements in the total layered process. I don't use cardboard here in Maine; the voles love it all too well.
I always water again as I make the layer of newspaper (at least 4 sheets thick) over the area. Without water, especially in dry regions, not much is going to happen in terms of composting and newspapers will fly away on any available breeze. I prefer to do this and the next step in conjunction, even limited time means I have to return to the task on another day.
Proceeding with the layers of compost, green/wet materials and brown/dry (carbon) materials, repeating the pattern of layers as I can obtain additional materials- I'm aiming to follow the general pattern of soil-building layers found in a self-regenerating forest/prairie/desert situation. Choices might include seaweed, grass clippings, coffee grounds, trimmings from vegetable and perennial gardens, non-meat food scraps, fruit tree prunings, animal bedding, spoiled hay or straw, cornstalks, sawdust, ground up leaves, pine needles, wool, hair, ground bark, torn or shredded newspapers torn cardboard, and chipped branches.
Local materials are desirable and may vary widely. They are often free or cheap or available for barter. I have a friend who drops off buckets of coffee grounds from a village store. My blueberries, rhododendrons and persimmon tree have appreciated that! Lime or other amendments can be added as needed to reach a healthy soil balance according to the needs of your planned crop. Layers may be thicker or thinner depending on the need for slowing or speeding up the composting process. Water or not as needed by local conditions and materials.
Like any compost operation, the height of the area will drop as materials are consumed, so the initial sheet compost area needs to be higher than the finished garden will be. For me, best results are achieved when I can give the new garden a season or more to cook down and mix with the help of earthworms. Even so, when making an ornamental garden in the autumn, I might set in spring bulbs. If the garden is for vegetables, I might spread a couple or three inches of finished compost on top for planting some crop seeds right away.
This is a long term approach requiring some initial and ongoing effort. It may or may not be the preferred method for all gardeners or situations.