The issue isnt the weight... its the amount of flex and that depends on the accuracy you want to achieve.

Remember that the cutter, router and mounting at the lowest part of the Z motion is acting as a lever trying to bend the z-rails. Assuming you are cutting wood with a typical router and a 6mm cutter you will be pushing something like 100N sideways force at a distance of say 200mm which is a moment of 20Nm (torque). That will flex 12mm unsupported rail by about .06mm and will result in a deviation of the cutter point about 0.6mm. If you are OK with that worst case inaccuracy then fine but even for wood thats high. 16mm rail will give a worst case deviation of 0.15mm, which is better.