The greatest demographic change in Asia during this time period was the rise of the Mongol Empire as is noted in Post #6. The Mongols established the largest empire the world had ever seen, even larger than that of Alexander. During their reign, the Silk Roads became a profitable means of trade again, as they policed the roads and prevented robbers, etc. from interfering. Because the Mongols did not trust local people, they often brought in people from other areas to assist in administration. They themselves were not fond of administration, they were fighters, not governors. An interesting element is that they insisted that the Chinese, where the Mongols held a large Empire, remain segregated from the Mongol population. The Chinese were forbidden to learn the Mongol language, were forced to dress in a separate fashion, and also required to wear their hair in the long pony-tail fashion known as the queue.
The Mongols also exercised some limited control over Russia, but not over Thailand, Vietnam, and other forested areas, as their horses did not function well when not on the steppes of Eurasia. Their Empire might have extended further (European powers could not stop them) except they abandoned their conquest of Europe when Genghis Khan died.
During approximately 700-900 C.E. The Mongol Empire was one (along with others like North African Muslim Empire) that developed more sophisticated economic and political systems as a result of the increase of world and local populations.
You might find it useful to revisit your question or thesis and consider what it is precisely that you need to do. Asia is such a vast territory that it is very hard to come up with any meaningful information. Are you comparing demographics with the demographics in Africa during the same period, as your other discussion post suggests? If this is the case, you might want to think again about whether this question needs to be narrowed down or tightened up to make it more specific and help you in terms of carrying out your research.
In trying to do some research on this topic using Google Books, I discovered that it helps to use the phrase "pre-modern" to find the kind of information you may be looking for. It also helps to be as specific as possible about the place you are trying to research. Thus, "India" or "China" is better than "Asia," and "Beijing" or "Delhi" is better than "India" or "China." You might also look for sub-categories of people, such as "women" or "men" or "workers."
Here's one link I found that may be helpful to you:
Interestingly, in this situation, searching on Google itself may be even more helpful than seraching Google Books:
One thing that seems clear from many of the sites I consulted is that firm information about demographics for Asia during the period in which you are interested is very difficult to come by. This is the case, of course, with all the premodern societies, whether in Europe, Africa, Asia, or the Americas. For this reason, you should be very wary of relying on any particular source and should try to consult as many as possible to learn about relevant debates.