Chinese paper for calligraphy and painting is very thin and the slightest breeze can send it flying. That’s why you need some kind of paperweights. Just about anything will do, from a few pebbles to these fancy hardwood weights I bought in Hangzhou, PRC. You can find something similar at most Chinese art supply stores (see: Links).
One nice feature of this style of paperweight is the rounded cross-section, as you can see from the bottom of one of the paperweights in the illustration. The concave underside reduces the amount of material resting on the paper—one edge lays on the table while only the other edge lays on the paper.