What typfaces are there that I can use varied weights for East Asian Characters?

I can't help you with Korean.  As for Chinese, the system fonts for Windows and the Chinese fonts bundled with some Adobe products come in a single weight, as you already know.  However, some of the Japanese fonts bundled with InDesign come in multiple weights: various weights of Kozuka Pro _might_ work for traditional Chinese, though some forms occur only in Japanese.

     Character set is a big deal, and Chinese fonts vary significantly in the number of characters they contain.  Typically, you get more characters in standard weights (i.e.,  "regular" or "light").  Note, too, that authors frequently use Windows system fonts for Chinese (MingLiU or PMingLiU). These happen to have very large character sets, meaning they contain many variant forms that are not available in most fonts; inevitably, authors use some of these variants and they show up missing in the weight you need.

     Dynafont and Arphic packages are pretty well regarded, and included a variety of weights in some styles -- but watch out for character-set issues.  I can't recommend a source since the one I used disappeared.

Good luck!

David