Many thanks to you all for your replies and thoughts, all very much appreciated.
The stand is quite flimsy and what I think is happening is that the lathe, being heavy cast iron construction, pulls the stand to conform to the shape that the underside of the lathe has. The amount of twist in the bed is quite small and this is noted with a bar held in the chuck at headstock but not supported at tail end, just making DTI measurements along the bed.
To eliminate the small amount of twist in the bed (only a few thousandths – I forget the exact amount), I've put shims between the lathe and the stand. What seems to be happening is that this bends the stand a lot more than it bends the lathe. The net result is that one corner of the stand lifts off the floor, making the whole think rock when given a push.
Even though the twist reads only a few thou, it needs a stonking great shim (2 mm) to eliminate it, again I think this is because the stand hasn't got the strength to fight against the lathe stiffness, so the lathe more or less stays where it wants and twists the stand, unless the shim is big enough to put some real stress into the stand.
What I think is needed is a way to prevent the stand from lifting one corner (preferably preventing it lifting any corners at all), which is why I thought of bolting it to the floor or weighing it down. Then, when shimmed, the lathe will have to twist itself or twist the stand together with the garage floor as well, which is considerably heavier and not very flexible at all.
I don't really want to move the lathe off the stand as it weighs so much, otherwise reinforcing the stand could be a possibility.
I think I'll have a go at bolting the stand to the floor and see if this improves things. I'll post the results when done.
Tony