Hi Wilfy,

Has requested cast my eye.!!

For an all steel structure it looks Ok thou I would replace the 50x50 with 50x25 to bring whole thing closer to Y axis plus gain 25mm travel.

The back plate which fastens to Y axis needs some cross bracing, just relying on the top bot plates won't be enough. Also Because your using steel this z axis will resonate quite a bit more than an Ali Z-axis would. So it would be wise to attach motor to ballscrew with a timing belt to eliminate any resonance problems, I would consider running that top plate back between the Y axis uprights so the motor is at the rear.
The 10mm plate is a bit OTT and 5/6mm would be fine strength wise and infact better if you take the route I've just suggested has 10mm is too thick because it shortens the motor shaft protrusion to much.

Regards weight then it won't be a problem for the screw it's the motor that you use that will take the stress but a 3nm will easily handle it.
3mm wall 50x25 weighs 3Kg/per Mtr

If you can use Alu then I would has it handles resonance better but what you have drawn will work fine.