The force of gravity on an object (its weight) is equal to the product of (the object's mass) times (the acceleration of gravity where the object is located).
In general, then, the object's weight is greater in places where the acceleration of gravity is greater, and smaller in places where gravity is smaller.
The acceleration of gravity (not the "force" of gravity) is greater on Planet Z than on Planet Y. Therefor, ANYTHING weighs more on Planet Z than it does on Planet Y. I think that's the second choice.