use of metal casing in small dc motors
The casing is the flux return path for the magnets. If you replace it with plastic, the strength of the flux through the coils will be significantly reduced which will reduce the torque production efficiency of the motor. This will mean you'll need a bigger motor for the same amount of power output, so you'll probably gain nothing. Of course, if the motor is already too powerful, then this might be an option. It is hard to estimate exactly how much the torque production will be affected, but it would be easy to measure using the back EMF.

If you need to reduce weight a better approach would be to use stronger magnets (so they can be smaller) and replace the iron paths with magnetic material (such as a Halbach array pattern). Iron paths are sort of like plumbing for flux, so replacing them with active magnetic material essentially reduces the proportion of the motor mass that is 'piping'. The ultimate embodiment of these principles is the coreless motor which is a copper coil suspended between two magnets. These motors have very high power density.

However, I would imagine any modification other than removing the case is going to be too difficult for your situation, so you might have to look at alternative motors.