Fix it to the floor, and it has the entire earth as its weight. It's not weight that's the problem. What you want is rigidity in construction. Whether you do it by large-section cast iron, fully-braced sheet metal, or even plywood is not as important as constructing it so it cannot distort in the load direction.
If you're not going to bolt it to terra firma, make sure the base extends ~50% beyond the swing perpendicular to the bed. Only needs the ends extended, not the entire, so you can make trestle type or, my preference, trapezoidal sheet-reinforced ends. This resists a good part of the off-center load by transfer. You can also weight the stand, keeping it where it does the most good - where it's widest. No sense making something with a high center of gravity even more unstable by putting weight up high.
All things considered, the best thing to do is to rotate pieces you mount freely, reduce the differences in weight by removing stock you'll have to remove anyway, so you don't have a huge imbalance. Don't neglect the possibility of boring some holes out of what will become the inside, or, if your creative vision demands something hugely imbalanced, boring out on the low weight side, weighting and re-plugging with some hot glue or washers captured by a lag. The better balance you begin with, the better your lathe will behave, and the easier it will be on the weakest point of the entire system, which might be your bearings.
