While I didn't have time to read all the responses, it appears to be just a layman's discussion of the possibilities. I'll still go by the MIT physics professor's answer. If anyone cares to contact an expert in this field, please post their response. (interesting problem though, eh?)
Edit: Let' try thinking about this problem from another perspective:
A 200 lb man is standing on the ground on a scale.
He jumps into the air & his weight is now measured at -0- lbs (electronically)
Where did his weight go?
I say it simply disappeared, negated by the force of his leg muscles propelling him into the air & was not somehow transfered to the air itself.
In a similar way, the bird's weight is no longer present (temporarily while it's in flight) as it is counteracted the lift created by its wings)
Or Another Example:
A rocket sits on the ground weighing 2000lbs
When its engines fire they create 2500lbs of thrust
The rocket start to lift off, but its weight is not simply pressing down against the ground or air via its exhaust since the rocket works just the same in the empty vacuum of space. (It's Newton's Third Law of Motion.....For every action, there is an equal & opposite reaction)
Therefore, the weight is not transfered, it simply disappears as a measurable force, according to Newton's third law of motion That took allot out of me....I need a nap!