The same reason you can jump up in a bus and not be slammed into the back of it.
The balloon already has the same velocity as the earths rotation. As does the air around it (ignoring air currents).
Lets take the bus example again. If you are in a bus, and it goes 50km/h, everybody else in that bus wouldnt seem to be moving at all. Because the bus is the closed system and you observe it from within that system. If you jump, it looks like you only traveled vertically, because you would land at the same spot on that bus. Why? Because you tarvel just as fast as the bus does.
Now, imagine someone from outside observing this. To them, you would jump and move forward at the speed of 50km/h.
You can view the earth and its atmosphere as a closed system.
Lets say you observe that balloon on earth, which means your point of reference is a point within the system. You wouldnt be able to notice earth rotation, because you rotate with it. Same goes for the balloon.
Now, lets say someone from the sun would look at that balloon. What would they see? They would see the balloon turn around earth with the same speed that earth rotates.
So you could say the balloon doesnt rotate with the earths surface, they just have the same velocity in the same direction, just like the air around the balloon.
To clarify, make no mistake. You do not rotate with the earth because you are attached to it. If that were the case, you would need to counter balance the 1000mph you mentioned evey second of your being. And I dont think thats humanly possible for even a moment. You just rotate with the earth seemlessly because you already have the same velocity.