Another suggestion to add to the pile: 安定 (maybe less for physical, more for mental/emotional balance?)
[MENTION=22184]allen[/MENTION]:
If you lost your 皿秤 , you should check the kitchen cupboards. This is why you shouldn't use Google Translate for anything but a laugh, especially between Japanese and English.
In most of these cases it's just that there are multiple translations depending on context, nuance, etc, and one happens to use katakana. Sometimes foreign-origin words (which not all katakana words are) become popular for whatever reason. Quite often they diverge from their source-language meaning in the process. It doesn't mean that there previously was no word for that concept, or no way to describe it, or reflect really anything much about the culture.
"Balance" came into English from French, but that doesn't mean that before the Norman invasion my distant ancestors didn't have some way of describing the associated concept(s). It would just have been different (or, since that's another French word, ungelic).
If you want to adapt your mindset to a new language, first throw away the idea that there are any simple "X means Y" relationships between words in different languages.
体勢 doesn't mean exactly "posture". It doesn't come with the same cultural baggage as might accompany it in English (for example, "posturing" in Japanese would use an unrelated word). When "posture" is listed in the dictionary for 体勢, it means the meaning of 体勢 overlaps with the meaning(s)/nuance(s) of the English word posture to a sufficient extent that it is sometimes useful as a translation, given the appropriate context. A good dictionary will have sufficient explanations/examples that you can understand what the appropriate context is.
I'm not sure what you're seeking. If it's a word that you can always use in place of the English "balance", there is no such beast. Not even バランス. Some you've listed are already described upthread. 対称 is close to "symmetry".
