If the earth rotates faster than its present speed, the weight of an object will : 

Decrease at the equator but remain unchanged at the poles

Centrifugal force

1. It is a force acting from the center of rotation outwards of a rotating body.
2. When Earth rotates, centrifugal force acts opposite to the center of rotation.

We know, weight of a body, W = mg

Where m is mass of the body and g is acceleration due to gravity. 

As the rotational speed increases, Weight of the body becomes.

W' = mg'

W' = mg - centrifugal force

where g' is decreased acceleration due to gravity.

We know, centrifugal force is maximum at the equator as the distance from axis of rotation is large over there and minimum at the poles where the distance from the axis of rotation is very less.

So acceleration due to gravity will remain same at the poles and decrease at the equator.

Therefore, weight of an object decreases at the equator but remain unchanged at the poles.