Most birds fly. To aid flight, avian bones are hollow, reducing their mass. In addition, bird wings and feathers are optimally designed for flight.
So why can't large birds or mammals fly? One of the problems is that they are too heavy to lift off the ground, necessitating unrealistically large wings to make it happen. However, it seems as if someone might have figured out how to design human wings for flight:
An analysis of whether or not this popular video is potentially real or fake is presented in a post from Rhett Allain, an Associate Professor of Physics at Southeastern Louisiana University, in Wired Science that you can access here.
If this isn't fakey, those wings have got to be filled with hydrogen/helium.
I vaguely recall reading a while back that someone actually went to the trouble of comparing weight of comparable size bird and mammal bones. They found no significant difference in weight, as I recall.