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Much of the struggle with terrestrial fusion power seems to be with keeping the ultra-hot plasma contained. In a classic Tokamak configuration, magnets using massive amounts of power, suspend the plasma in a torus that contains the incredible heat and prevents it from melting the containment apparatus. So far, this appears to be one of the great challenges and a reason why we do not currently have cheap, sustainable fusion power.

If you had a fusion reactor in geosynchronous orbit, it would seem like many of these problems of containment would be greatly simplified by weightlessness. The magnetic containment would just be needed to hold the plasma in place, but not need to hold it against gravity.

Another aspect to this might be if space elevators (aka know as 'beanstalks') are used as connecting conduits for bringing generated power back to earth.

What is the practicality of orbital fusion reactors as a source of energy and would weightlessness simplify containment challenges? Current terrestrial test fusion reactors need to be incredibly heavy and massive. Could they be lighter and simpler in space?

I think that as regards containing hot plasma, gravity is the least of their worries. Think how much mass in in that hot plasma. Probably hardly any because the less mass there is, the easier it is to heat it to fusion.

But lets figure it out with the hard hardness of hard science! Here are stats for the EUs fusion project.

https://www.iter.org/FactsFigures

The plasma volume is 830 cubic meters. Considering that volume of hydrogen gas at 1 atmospheres and 0 C I got 66 kg. I can lift that on a good day.

http://www.airproducts.com/Products/Gases/gas-facts/conversion-formulas/weight-and-volume-equivalents/hydrogen.aspx

But maybe this plasma is at high pressure? It looks like pressures are not super high.
From 2016: http://news.mit.edu/2016/alcator-c-mod-tokamak-nuclear-fusion-world-record-1014

The team set a new world record for plasma pressure in the Institute’s
Alcator C-Mod tokamak nuclear fusion reactor. Plasma pressure is the
key ingredient to producing energy from nuclear fusion, and MIT’s new
result achieves over 2 atmospheres of pressure for the first time.

So 830 cubic meters of plasma at 2 atmospheres. That would be double the weight or 132 kg. I would need help to lift it.

But the whole thing about a Tokumak is that it is hot; from first source, 15 million C. I am proud of the linked calculator; it would accept that value of 15,000,000 C. It gave me

= 3.2757271682719E-6kilogram/meter^3 or 0.0000032 kg / m^3. *830 m^3 that would be 0.0026 kg or 2600 mg. That is 10 grains of rice, which I can lift.

I conclude the force of gravity on the contained plasma is not much of a consideration. Really the consideration is keeping something that is that hot in a place where you can heat it up more.

I have been known to misplace a decimal here and there. Anyone feeling an itch to duplicate my math, I would like to know if I screwed something up.

Unfortunately, it's not at all practical. The basic issue is that the reactor (at least any reactor built with foreseeable technology -- Mr. Fusion is on the far side of Clarke's Law) is very, very heavy (making orbit a Bad Place to put it since costs are still around $3000/lb to put things into low Earth orbit and several times that to GEO), while the plasma itself weighs very, very little.

The ITER plasma volume is on the order of 2000 cubic meters and the plasma density is 0.6x10²⁰ atoms/cubic meter, so there is 1.2x10²³ atoms total, which (if it's using a deuterium-tritium mixture, which is likely for the first reactors, at least) is right around 1 gram.

Besides that, waste heat dissipation in space is very difficult, and a fusion reactor will produce a lot of waste heat. (Foreseeable designs produce more waste heat than usable energy.) The only practical method for getting rid of waste heat in space is through radiators, and that would be a significant chunk of additional weight...all of which must be moved to GEO at high cost.