[rrobson]

If the train is badly set up (as in weight in the wrong places) the weight of the tow vehicle is irrelevant, it’ll still throw it about. The advantage of a heavier tow car is it is more resistant to swaying, but it can still swing about.
If you’ve got a 2t vehicle and your towing a 1t caravan then you’ll likely not notice a bit of sway, you might feel it if it builds a bit of momentum. But weight isn’t the main factor, tyres, suspension, length and width of tow car, weight distribution of tow car can all have unusual outcomes to stability.

If you take the same set up and put a large proportion of weight at the rear reducing the nose weight, obviously it’ll swing a lot and it will be felt even in a large car. I had this when I was rescuing My 75 a few years back. My terrano weighed a smidge over 2t, and when I loaded the car up it was a bit too far back on the trailer. It was all over the place and it was really felt in the tow car. So rather than moving the car I moved the spare wheel from the well to the passenger seat and some bags of clothes on the drivers and that was enough to stabilise the trailer.

If you set the nose weight up correctly and distribute the weight in the caravan correctly it shouldn’t sway unless the outfit is mismatched. A heavy tow car isn’t an excuse for a bad set up but it can certainly help!