This one's far too easy- if the dowforce of air generated by the birds' wings is less than the weight of the bird then the birds will hit the floor. This is due to the no. 1 law of physics which states, "There is no such thing as a free lunch." The only way you'd be lightening the A/C would be to remove the floor of the cargo hold, in which case the plane would'nt be carring the birds but flying in formation with them.