Q:

Harvesting resources from a geostationary point 100km above sea level

Consider a planet which is entirely Earth-like. Same mass, same rotation, etc. But in this world, resource-rich objects are suspended by some phenomenon at varying altitudes up to 200km above sea level (effectively from the surface, since the highest point, Mt Everest, is >9km above sea level). Clarification: some are at 200km, some are at 5km, 50km... They are fixed relative to the planet's rotation, thereby always being above the same point on the surface. The resource is valuable, and must be harvested by a machine such as a modern backhoe loader (e.g. the arm on the back of a JCB digger).
How might a society with approximately our level of technology exploit these resources?
Up to perhaps ~10km, specialized helicopters or airships could be flown.
Anything at or above the Kármán line would pose a problem: the orbital period is 1 day, but the altitude and hence orbital velocity is far lower. An asteroid in a Keplerian orbit would be straightforward, if not cheap to harvest: a spacecraft could match its orbit. But in this case, if a regular spacecraft or spaceplane attempted to orbit at the same altitude, it would fly past the target very quickly.
Between the limit of helium balloons and the edge of space, there may be other problems.
How could people harvest the resources of the higher objects?

A:

Ballistic Trajectories
This is actually easier than getting to space. Space is hard because you have to go really fast to be in an orbit.
Achieving orbital height is easy. Achieving orbital velocity is hard.
So you build a rocket right beneath your "geostationary" resource, and give it just enough fuel to reach the height you need. Your rocket releases a payload, which has exactly zero velocity when it reaches your resource. The payload grabs on to an outcropping, or uses a harpoon, or otherwise attaches itself to the valuable thing.
Now, either the magic that keeps the resource in the air keeps your payload in the air, and it starts harvesting, or the whole thing is now too heavy for the magic and it falls towards earth, in which case the payload controls the landing.
This is hard, but not as hard as actually harpooning an asteriod, which we have done.

A:

Send impactors against them to reduce their momentum. They will lose altitude. After they descend some the increased atmospheric drag will cause them to deorbit and crash. You'll just need picks and shovels then.

