Towing a caravan

Thank you for the advice.

Do you know if the Jimny stability control will activate to assist when towing a caravan, if the outfit gets into a sway?

The truth is, as much as it hurts me to say this, the Jimny is not a good tow vehicle. Yes it can do it, but so can my 2CV (yes it has a tow hitch). That's my point, just because it can does not make it good.
The G4 addresses one issue which is a real lack of power, but I can't comment by how much that 200cc will help. Any sort of hill is going to see 4th/ 3rd and 40mph max, motorway speeds 50 / 55 on the flat. Stability is not an issue, it always feels in control (at the above speeds), but the fidgeting nature of the ride is double as you now feel every jolt of the road. 
This is my G3 with no more than 750Kg on the back. 

This is of course just my opinion, based on the many miles I tow my caravan with my G3. 
In fact on holiday now, 360 miles just completed.
I put up with the poor towing experience as I simply like the Jimny, just wish I had 2ltr and a turbo for the days it has the van attached. 
 

Proof a Jimny can happily tow a caravan or load, braked upto 1300kg. Enjoying the journey is down to your expectation.

Summary 
Yes it can tow a caravan. 
Lack of power is the main issue, at some point you will be travelling slowly on a fast motorway. 
50mph is about it on the flat. 
Stability is not an issue, its very good if you load the van correctly. 
 

That's a new one, a fast motorway , most in my neck of the woods are controlled from overhead gantries and those that aren't are gridlocked anyway. But, coming back to the main point, tow a caravan and you are restricted to a max. of 60 mph so doing a max. of 50 in the inside lane is not such a bad idea. 

Not so sure about being overtaken by an artic. though.

Roger

I regularly tow with my Jimny (gen 3 manual, 1.6 swap, auto diffs)
​and with a balanced 1,300kg load in a single axle 8'x4' trailer it is very stable. Given the size and weight of the car, I'd say it tows exceptionally well. Your issue with the caravan will be the sheer size of it. Extra wind drag will sap power and also make it less stable. A 7ft wide trailer behind a 5ft wide car is not a good combination in my mind.

I have an Ifor Williams P5 trailer and used it to tow a few loads of heavy 100 old bricks. About 140 bricks per load. It was sat down a little but it did ok. Just take it nice and easy and don't do anything silly.

You might find a better tow car for the money but you won't find one for the size apart from maybe a super short ibex.