10-20 kg, call it 25 per drawer, with 4 drawers, that is about 100kg, which would require 15mm diameter wire, which would exert some give under the pressure of 1000 newtons, however 2 cm diameter wire would remain more ridgid. the exact design is up to you, but if you go with 8 drawers, you would need 2.5 cm wire, and 16 drawers would need 3cm wide wire. I assume that you are talking in cm for your dimentions, as 143mm would be too small for anything of such a mass, right?
If in doubt about the size needed, go up a size.
as for making the hexagonal mesh, you either need a lot of time for cutting steel (not fun) and welding, or access to a maching capable of exerting about 5 tons of pressure to cleanly bend the wire to the desired shape. With the amount of work you would have to put in, I would consider just buying a filing cabinet.