There are two ways that the manufacturers of these lightweight cabs make them lighter. The first is by using drivers with neodymium magnets. These are equivalent in every way to the more familiar, heavier drivers and the weight saving is made possible because of a technological advance. Neo drivers are roughly half the weight of their ceramic equivalents. They are also twice the price.
The second way of reducing overall weight is by reducing the weight of the cabinet. Because there is no technological advance involved here (such as carbon fibre panels, for example), manufacturers make the cabinet walls out of thinner or less dense materials to get the weight savings. It's fairly obvious that this is not ideal, because the cabinet is going to 'talk' when pounded with bass frequencies, but many people are prepared to accept the compromise to get the light weight. I may be wrong, but I have the distinct impression that most of the people buying these have bad backs.
The PA industry went throught a similar kind of thing several decades ago when the plastic PA cab was introduced. Most of them make the singer sound like he is singing in a bucket, but they remain popular - especially with female vocalists. It interesting to note, however, that PA bass bins are almost without exception made from 3/4" stock because that is what has proven over many years to be optimum.
A good, modern conventional cab will always outperform a modern 'lightweight' cab of equivalent price - especially at volume.