Going on typical weights, the heaviest flying bird is the kori bustard, which can weigh from 11–19kg, followed by the great bustard (6–18kg), the mute swan (6–15kg) and the Andean condor (up to 15kg). Because of its tremendous weight, a kori bustard uses a lot of energy to fly, so it will only take off when necessary.
The theoretical limits of maximum body weight for horizontal powered flight are in the region of 10–15kg. This means the largest male bustards are, technically speaking, exceeding the boundaries of what should be possible!
Main image: kori bustard © Getty Images