Most laser cutting machines are 3-axis systems, that is X-Y, two dimensional positioning control with a Z-axis height control. There are however a number of ways of achieving the X-Y movement, either moving the laser head, moving the workpiece or a combination of both.
The most common approach is known as a 'flying optics' system where the workpiece remains stationary and mirrors are moved in both X and Y axes. The advantages of this approach are that the motors are always moving a known, fixed mass. This can often be much heavier than the workpiece, but it is easier to predict and control. As the workpiece is not moved, this also means that there is no real limit to sheet weight. The disadvantage of flying optics is the variation in beam size, as a laser beam is never perfectly parallel, but actually diverges slightly as it leaves the laser. This means that without controlling the divergence, there maybe some variation in cutting performance between different parts of the table, due to a change in raw beam size. This effect can be reduced by adding a re-collimating optic, or some systems even use adaptive mirror control.
The alternative is a 'fixed optic' system where the laser head remains stationary and the workpiece is moved in both X and Y axes. This is the ideal situation optically, but the worst situation mechanically, especially for heavier sheets. For relatively light sheet weights, a fixed optic system can be a viable option, but as the sheet weight increases, accurately positioning the material at high speed can be a problem.
The third option is known as a 'hybrid' system, where the laser head is moved in one axis and the material moved in the other axis. This is often an improvement over fixed optics, but still suffers from difficulties with heavier sheet weights.
In conclusion, a flying optics system is ideal for heavier sheet weights, but care is needed to control the laser beam divergence effects. For lighter sheet weights, a fixed optic or hybrid style laser can offer some benefits.