the language of the horse is body language and pressure
Absolutely and isn't it great that they can understand our body language, despite our lack of twizzly ears and swishy tail? :lol: To be really natural our horses should buck like crazy when us predators get on their backs, it's brilliant that they are so willing to become partners with us and let us sit on them isn't it?
When it comes to our balance, it's our responsibility to sit as straight as we can and to move with our horses, so as not to put them off balance. For young horses just learning to carry us, our posture is so important to make it easy for them to balance us on their backs. When I'm teaching someone, I might ask them to put a little more weight one side than the other and use various exercises, to correct a rider who is riding with an imbalance, but on the whole, I obviously agree with Heather and feel other than trying to remain stable and centred, actually deliberately thinking about weighting isn't always necessary or useful.
However, it is fun to experiment with it and find just how we can influence our horses with our weight and it's useful to know so that we can correct ourselves when our horses tell us we're wrong, just as you're doing ST.

If you can get Heather's book, or read any articles she has on 'turning aids' for example, there's a lot more there about hips and seatbones and what we can try to best aid our horses and make it easier for ourselves. She explains it in a really good and simple to understand way, that I've got no chance of matching!
Keep us updated with your experimentation though, won't you? I for one am finding it really interesting to discuss. B)