Some times I'd love a variator. I have a big hill to get to my house that requires some forward planning and a bit of luck with the traffic to get up!

Is it possible to fit one on a dimoby moped or do you need hefty modifications?

Difference between a dimoby Model L and a 50 V variated clutch mobylette
Rear (wheel) sprocket tooth count (L=44 V=54)
Front (pulley) Sprocket tooth count (L=13 V=11)
Chain length (approx. L=92 V=104)
Belt tension spring (V spring is much stiffer)
Spring retaining clip (V has a longer hook)

You need a stiffer spring , you can keep the pulley and wheel sprockets, it will go faster on flat surface if you want, to climb you'd need the 54 big sprocket, and of course a longer chain.

I don't have a spring at all. My belt is tensioned by rotating the engine manually and a bolt tightened to hold it tight. What does that mean?

Look at this picture, this is the spring that keeps the tension on the engine.fig3
This is for Motobecane mopeds, I'm not sure your model is the same. Sorry
Someone with knowledge of your particular model should be able to help you.

The RM4 has the Dimoby set up without the springs. The frame has a solid mount which bolts directly to the lower exhause/engine mount and there are top isolators for vibration dampening similar to a variated engine.
What you would need to change the configuration would be a snubber to replace the lower mounting so the engine would be able to swivel on the upper mounts. The snubber would need to have a spring strong enough to partially restrict the swivelling of the engine so that the variator would change the gearing progressively between 2500 rpm and 5500 rpm.
I made a linear snubber spring for the Cady Speedster as that had a similar solid mounting for the Isodyne motor. It took a little messing around with springs and such but it does work quite well.

A job well done by the looks of it!
Is the variator easy to fit onto the engine? Would it be a direct swap for the dimoby?
Presumable I would have to get a different exhaust too- one that is mounted only on the engine?

You would be best suited to get a complete donor engine for the variator with related hardware and the exhause plus mount.

a long time ago, I made this modification.
My N40T was too slow ans I was always behind at each traffic light...

I take the variator from another engine (don't forget the screw) and I had to make some few modification.

the intake pipe was too long, I had to take a shorter one, and the black air filter (quite a squared box) has been changed for a triangular one.

the exhaust pipe (a round tube chromed with a muffler with an oval shape) has been replaced by a standard one
I never had to change the springs, I left the sprockets as they where...and it still works fine 35 years after

here are the two exhausts models:
http://bibliotobec.org/gallery/picture.php?/1146/category/148
and the two carburetors:
http://bibliotobec.org/gallery/picture.php?/1151/category/148
http://bibliotobec.org/gallery/picture.php?/1150/category/148
and the two intake pipes:16619 for the variator and 21201 for the dimoby
http://bibliotobec.org/gallery/picture.php?/1144/category/148