contain, hedge and balance?

Contain means to limit (in this context); i can't imagine anyone using hedge in such a context--it means to limit or qualify, but not in the sense of a nation's economic growth, but rather in the sense of an individual or a group limiting their potential losses. People in a hedge fund, for example, usually invest borrowed money in a high risk/high yield venture, so that their capital assets are not at risk. I also cannot think of a reasonable use for "balance China's rise," it implies an outside agency. Even if other nation's think China's policies are stupid, they are not in a position to do anything about it.

With regard to "China's rise," contain is only one of these three verbs which makes sense.

A prize for the best joke here about the Great Hedge of China.

Thank you so much! However, there is report by CFR which did mention "balance China's rise" and I'm trying to figure out the difference from "contain".

If you mean the Council on Foreign Relations, that would likely be by a native English speaker. Otherwise, i have no idea what you mean by "CFR." Who or what will balance China's rise, and what is meant by China's rise? This why it is important to provide context when you ask a question. At the very least, the entire sentence in which an expression or phrase appears will help. Some people here will do a web search for the context. I'm not inclined to expend that sort of effort myself.

Sorry for not providing the context.
It is released by Council on Foreign Relations and argues that the United States should revise its grand strategy from integrating China to balancing it.

Here, "balance" would mean to counter, to match.
"Contain" would probably mean to control.