To remain aloft, the fly is exerting a tiny downward force which the plane's engine must compensate for. This is a slightly greater force than the fly's weight, due to the inefficiency of transferring energy to air.
Here's an extreme example to demonstrate this Conservation of Energy principle:
Imagine a large hot air balloon flying overhead with a flat platform on top. A harrier jet is parked on this platform, so the balloon is supporting its weight statically.
When the jet begins to take off, it exerts a downward force equal to its lift, in the form of air movement. The balloon is pushed downward in response to the force needed to launch the harrier.
On a much smaller scale, same with the fly.
The other part of the question is more complex. If the fly is partially outside the plane then it is certainly attached to the plane, contributing its own weight in addition to some drag. Considering the speed of a plane, this effect may be substantially greater than the fly's weight, at least for the few milliseconds before wind shear causes the fly to disintegrate