Question

Why does the weight of an object differs on poles and equator?

Answer 1

There are two reasons for this -
1) Earth is not perfectly spherical.

It has less radius on poles and More on equator

So due to less radius on poles the gravity experienced is More as the surface is closer to the center of earth compared to the equator.
as you can see if radius of earth increase, the gravitational force on body decreases.

2)

Second reason is that Earth is spinning with more angular velocity at equator are it decrease as we move towards the poles.

This increased angular velocity at equator produces a force a outward centrifugal force which decreases the effect of g.