This is a common question (it usually arises and gets subsequently analysed over a pint of beer) ......
Clearly none of you are helicopter pilots .... or if you are, remind me not to fly with you
(For the record I'm fixed wing not eggbeater)
Newton's third law states :
Every action has an equal and opposite reaction
Therefore, in the case of a hovering bird (or helicopter) :
Lift = Weight
(Thrust = Drag to be pedantic, but I've assumed the birds are hovering)
The fluid (i.e. air) that the bird now occupies has been displaced (ref. Archimedes for a nice example) .... but the aircraft is a sealed environment (ok ... so we've got AC Packs drawing in bleed air but I've assumed they are recycling air).
Therefore there is no difference in weight.
......... bows and exits stage left
You didn't mention what the prize was for the correct answer ...