Most of what follows is scientifically dubious. I'm looking to clarify one aspect and one aspect alone.

A small planet is being terraformed by an alien race who have been doing this for millennia. They proceed by wrapping the planetoid in non-permeable, initially flexible, transparent, indestructible unobtainium.

Then they inflate the resulting balloon using gases they have brought with them in liquid form. The resulting balloon has a diameter approximately a mile more than the diameter of the planetoid. This is their standard method. They always choose small planetoids and make the balloon the same height above the ground. The balloon is pressurised and the density of the unobtainium is more than that of the atmosphere it surrounds. The pressure is such that the surface of the balloon becomes very taut like a balloon about to burst.

Their purpose is to farm the entire surface of the planetoid.

The planetoid does not have any substantial satellites - only small alien-made ones. It is circling around a Sol-like star at a Mars-like distance.

Question

Given the conditions above, will the balloon remain concentric with the planet or will it tend to brush the ground at times?

My belief is that it will self-stabilise because atmospheric pressure will be greater at lower altitudes and so push the balloon away if it drifts too close to the ground. I also believe that it will end up spinning in the same direction as the planet and thus perhaps be flattened somewhat at the poles.

Am I right that it will self-stabilise or do the aliens have to have some extra mechanism to keep it from touching the surface? Might the solar wind be a destabilising factor? Would it help if the unobtainium was non-flexible? Would increasing the height above the ground provide a more significant pressure gradient (thanks Alexander)?

If it isn't self-stabilising then suggestions for a minimal change to the system to make it stable would be appreciated.

Reminder

The balloon is made from non-permeable, initially flexible, transparent, indestructible unobtainium.

Have you ever wrapped a gift for your girlfriend/boyfriend in a balloon?
If you have done it, or have at least seen the thing, you should have noticed that the pressure in the balloon doesn't keep the gift in the middle of the balloon.

You simply have a body immersed in a fluid, which will then experience the usual buoyancy force. Since the planetoid will be subject to the gravitational attraction of the main body (I assume it is the central star), that won't displace the planetoid with respect to the wrapping.

However, your aliens, in order to wrap the planetoid, must have matched its orbital velocity with the velocity of the wrapping. So it is safe to assume that the center of mass of the planetoid and the center of mass of the wrapping are moving in the same way. If they didn't do it, the planetoid will simply burst through the wrap at some km/s. So my suggestion to the alien is: match the orbital velocity of the planetoid! Then orbital mechanics will take care of the rest.

If they didn't bother in setting up a rotational regime coherent with that of the planetoid, what will happen? The atmosphere in the wrap will be initially at rest with respect to the wrapping, except for the layer in contact with the planetoid surface, which will be drag around. This drag will then transfer to the outer layers, until the entire wrap and the enclosed atmosphere spin coherently with the planetoid.

The force that the planetoid and its atmosphere exerts on the balloon is a combination of air pressure and gravity. Assuming that the atmospheric pressure is comparable to Earth's, the pressure on the balloon is 14 lbs/square inch outwards. I have no idea what the weight of a square inch of unobtanium balloon materials is, but since the question has the balloon stay up, we can assume it's less than that, and the balloon can be kept aloft by atmospheric pressure.

Now, ignoring gravity for the moment, consider the tightly inflated balloon. The outward pressure on it is due entirely to the atmospheric pressure at the interior surface of the balloon. And that atmospheric pressure decreases with altitude. So the higher up a piece of the balloon's surface is the lower the outward force from air pressure and the lower the balloon's surface is, the higher the outwards force. This is exactly what's needed to center the balloon.

But how big is the force? That depends on the lapse rate, the rate at which atmospheric pressure declines with altitude. Here the fact that it's a planetoid works against you.

The equation for atmospheric density (or pressure) as a function of height is d = e ^-kgh where k is a constant, g is the surface gravity, and h is the height. A lower gravity means that density (and hence pressure) declines less rapidly with height. The height at which atmospheric pressure drops by half is inversely proportional to the gravitational binding and thus to the mass. The half-height for Earth is about 3.5 miles. Ceres (the largest asteroid in the Solar System) has a mass of 0.0002 Earth, and consequently has a half-height of 17,000 miles. Smaller planetoids would have correspondingly larger half-heights.

So we have a planetoid inside a pressurized balloon of air. The lapse rate of the planetoid is so small that it would make an infinitesimal difference in the atmospheric pressure over the mile from planetoid surface to balloon, and consequently, there would be only a small restoring force tending to keep the balloon centered on the planetoid.

Now bring gravity back into the picture: Since we have assume that the air pressure exerts a greater outward force on the balloon's surface than the inward force due to gravity, we can call the balloon a sphere. Newton himself proved that a uniform spherical shell of matter exerts no net force on an object inside it, and the object inside it naturally exerts not net force on the shell. So as long as the shell is inflated by air pressure, the gravity of the planetoid has no effect, and exerts no restoring force.

Bottom line: You'd have a spherical balloon of air with a planetoid drifting around inside with no particular tendency to stay in the center.

I think you will need some kind of alien stabilization technology. Imagine a tennis ball inside a large inflated balloon. The pressure of the air inside will not keep the tennis ball from bouncing around, even in zero gravity. On a planetary scale the rocky planet still needs to spin and orbit its star, so the planet-sized balloon would have to keep up with the orbiting planet, using some kind of propulsion system.

I think a better technique for terraforming is to understand how Earth keeps its own warm atmosphere from leaking out into space. It's really quite simple. It's just gravity. Gravity keeps the air molecules on our planet. Our planet also has a spinning core of molten iron which creates an electromagnetic field around our planet, protecting it from solar winds which might strip away our ozone layer and atmosphere. The aliens would only have to pick a sufficiently massive planet, fill it with their preferred atmosphere, and generate a protective electromagnetic shield. No balloons needed.

Action and reaction

If inflation is slowly uniform the system should be self centric.

As the envelope approaches the surface on one side the opposing side moves away, so once evenly pressurised a self compensating balance is reached.

What could create a calamitous wobble with a catastrophic collision is significantly uneven internal weather, or a drastic external collision event.

In either case the "skin" would brush the surface and the whole system instantly collapse.

Solar wind will blow the 'wrapper' into the planet

Solar wind is a stream of charged particles blowing from the sun out into space. At a distance of 1 AU, pressure from the charged particles is in the range of 1-6 nPa. This isn't much, but integrated over the surface of a planet this will cause significant deformation of your shell. It will not remain perfectly concentric.

... also, about that solar wind ...

Solar wind is mostly composed of protons. Therefore it is positively charged. If the solar wind impacts on the shell, the shell will eventually be positively charged, since protons will strip off electrons. This will turn your entire system into a giant capacitor. Eventually, the voltage across the capacitor will be high enough and then ...

Does your planet have a magnetic field?

Back on topic, an electrostatically charged shell around your planet is bad for other reasons. Does your planet have a magnetic field like Earth does? Well, then you will get a Lorentz force vector based on the motion of a charged object in a magnetic field. Even if your planet's magnetic field is perfectly symmetrical, the shell won't be, thanks to solar wind, so there will be some asymmetric magnetic forces pulling on the shell.

The direction of the force will vary depending on the magnitude of the magnetic field, the distance the magnetic field extends from the planet, the distance of the shell from the planet, etc. There is also the possibility of relative motion (even if it is minor) between the shell and the planet. All of these factors will be significant, so I'm not prepared to estimate the magnitude or direction of the magnetic force on the solar-wind-charged-shell. But it won't be zero, so your shell is going to move.

Conclusion

The shell is going to hit the planet, one way or another.

Better idea though, what is wrong with using gravity to capture things on the planet's surface? Gravity is, after all, what kept our atmosphere attached to us for the last few billion years. A 'gravity well generator' that you put your planet into to prevent things from leaving the surface isn't any less realistic than magical handwavium shrink wrap on a planet.