I want to buy a lightweight silk jacket while I'm in Beijing at the end of the month. how?

You can go to the Silk Market to have a look. The price is hard to tell, because it is different according to different quality of the silks. There are many silk shops in the Silk Market and you can wander and company. Generally speaking, a well quality coat costs around 1000RMB or more.
For buying such a coat, it is suggested to get a one tailored based on your size.

If you cannot find the suitable fabric, you are suggested to go to Shanghai to have a look.