Effect of gravity vs airmass on a falling object
This answer assumes that the wind is uniform in direction and speed, from the balloon all the way down to the ground.

The object will impact the ground directly below the balloon, not "upwind" of the balloon.

As the falling object accelerates vertically, the trajectory of the falling object as viewed from the ground reference frame continually becomes more and more perpendicular to the ground.  Yet the horizontal components of airspeed, force, and acceleration are all zero throughout the entire fall, so the falling object remains directly under the balloon.  

As viewed from the airmass reference frame, the trajectory of the body is purely vertical, i.e. completely perpendicular to the ground, throughout the fall.  

The horizontal component of the object's groundspeed is constant throughout the fall, and equal to the wind speed.

Now imagine simultaneously dropping a low-density object and a high-density object from the balloon.  Both would be directly below the balloon at the moment of impact, but they would impact at different times.

For more, see Force Balance from Wind

Also, note that saying the object will tend to fall straight down relative to the earth, rather than relative to the balloon and the airmass, is essentially saying that the earth is a privileged reference frame, which goes against the laws of physics.