How about:
Weight refers to the force of gravity acting upon an object near the surface of the Earth. Whereas the apparent weight is the force experienced when the force of gravity and normal force an not balanced, therefore resulting in feeling heavier or lighter.
I think you've misunderstood what I was trying to say. You feel apparent weight whenever a normal force is acting on you, INCLUDING when the normal force and weight force are balanced. The magnitude of this normal force (and hence the magnitude of your apparent weight) changes when the normal force and weight force are not balanced, but it is also there when the normal force and weight force are balanced.
When the normal force and weight force are balanced, apparent weight has the same magnitude as actual weight. When apparent weight is not experienced, the normal force is not acting on you.
Gravity can act even when not near Earth and force due to gravity in these situations is still referred to as weight