There's nothing wrong with taking up the amount of space you actually need, whether because you're fat, have broad shoulders from weight lifting, or for any other reason. But humans take priority over stuff.
In that case, I might have asked the woman to move her purse, but if I then looked at the seat and didn't think I would fit, I would say something like "thanks anyhow, but I don't think I'll fit there." However, it was absolutely reasonable for you to sit as best you could, even if it meant perching on the edge, and rude for that woman to try to push you off. She may well have needed one and a half seats, and if so, it's fine for her to take that much space. Not to insist on the other half seat she hadn't been sitting in.