If we go deeper inside the earth, what will change: weight or mass or both, why?

As we go deeper inside the earth weight of object changes and mass remains invariant.

Since, mass of an object is the amount of matter contained in the object and as we know that going deep inside the earth will not change the amount of matter contained in the object, so mass remains constant. In fact mass of an object always remains constant and does not change from one place to another.

On the other hand, weight of an object is the force with which earth pulls an object towards its centre.

W = m × g

From above, as we know that g decreases as we go deep inside the earth, so the value of the weight of the object also decreases.