Probably the thickness of the strokes is important only to the esthetics of the writing and has nothing to do with the meaning.

That's pretty much how I see it. Aesthetics can be important, but usually not for semantics. Language is a messy thang. One thing that Chinese do sometimes when discussing characters is to "draw" them in the palm of their hand with their index finger. (Heck, I've done it myself with success.) It's the order, number, and position of the strokes that's important in that case.

Another "myth" about Chinese is that it cannot really be represented by some kind of phonemic writing system, like pinyin. This is just so much poppycock. When speaking Chinese there is usually no recourse to characters; in fact, there are—gasp—illiterate Chinese who speak the language daily.