like said above- momentum- when going up you only pick up your weight (your mass times the acceleration of gravity), on the way down you have to stop the acceleration of gravity plus that of you "falling" the height of a step.
Try lifting a bowling ball up 24 inches versus catching one dropped 2 feet. Catching the dropped one is much harder.
My personal favorite is when i hit calves so hard i cant even muster enough strength to push the pedals of my car. I just end up eating dinner at the restaurant next door.
cant say ive never done that, ive almost tripped going up stairs when im delivering pizzas cuase my legs are to tired tp pick up all the way. makes them feel sorry for me and i get a bigger tip