Of all the birds that have the ability to fly, which one is regarded as weighing the most?

The heaviest flying bird is the great bustard which weighs up to 46 pounds (20.9 kg).

http://www.enchantedlearning.com/subjects/birds/Birdextremes.shtml

I thought it might be you or Bedstor that would get this one, Jenny. Good job.

"175 years after it died out in the UK, UK conservationists plan to reintroduce the Great Bustard, which is the world's heaviest flying bird. The bird was hunted to extinction in the UK because of its meat in the early 1830s." - UK Plans To Reintroduce World's Heaviest Flying Bird
Ah! A nice Bustard au vin ! Or just simple fried bustard. (Who gets the drumstick?)