Is it possible for a body to have inertia but no weight?

(N/A) Yes,it is possible. Inertia is a property of a body determined by its mass $(m)$,which is an intrinsic property and remains constant regardless of the location. Weight $(W = mg)$ is the force exerted by gravity on the body. At the centre of the Earth,the gravitational acceleration $(g)$ becomes zero. Therefore,a body placed at the centre of the Earth will have mass (and thus inertia) but its weight will be zero.