On the strength issue, women have stronger legs and a lower centre of gravity* so I find the idea we can't carry heavy loads to be rather far fetched. The problem is we aren't expected to carry heavy loads and are told not to in fact (I was carrying a large box of books around at work quite recently and some random woman came up to be and told me off for carrying something heavy because I might damage my uterus...) so we aren't conditioned to carry heavy loads and build up muscle like men are. I saw a survey quite recently actually which found that once we hit puberty something like two thirds of girls tend to stop sports and other physical activities due to body image issues.
*So patriarchy values upper body strength more, funny that...