As a broad indication of mid to late 20th century Chinese manufacture, the base of many of their paperweights shows an uneven base finishing (not properly round, or round with an obvious indent) which is also rough ground rather than smooth and polished. But newer Chinese (and Taiwanese) weights can show much improved finishing with many being smoothly polished and well rounded.
Also note that a rough ground base does not mean something is definitely Chinese. Lots of modern Studio makers around the world use a rough grinding for finishing. Also, a base that is not properly round can be found on some modern studio pieces, too.