Reverse the Question

Nature/Nurture aside, I think most of the things you hit on, 'look huge', 'play sports', etc are socialized instincts. From a young age you are continuously being socialized to accept certain things and not accept others. Little girls are way more dressed up than little boys, just go to any department store and look at babies clothes. You will find much more for girls and they are usually much more sophisticated than the T-shirts and onesies that boys wear. We imprint such behaviors on little kids. How often do you see a parent fussing with a little boys hair? How often do you see little boys being given dolls and told to put fake make-up on them to look more pretty. We socialize our girls to feel insecure and crave make-up, dresses, large breasts, and flawless skin. It's not about mating, but about feeling secure and a sense of belonging.

I don't know if you are an inboard or an outboard, but as an guy, I can say I work out primarily so it is easier to fornicate with the more desirable of the girls I encounter. (Needless to say, the recent goth/emo do beguile me.)

Also, many guys find extra strength/ability handy in the 'tasks' we are traditionally expected to be good at. This would drive the desire to work out.

As for sports, I figure we play them for the same reason women do: they are fun.