Explanation:

The solution can be understood in a very simple example ,if we are travelling in a car and it takes a left turn we r pushed towards right ,here the force acting is the centrifugal force which pushes the body outwards
    Similarly for a body on the surface of the earth ,if the earth rotation increases the centrifugal force will be acting to each body to throw it outward ,but due to gravity it will not be thrown off.
    WEIGHT=mass×g(acc. Due to gravity)
    But in this case,weight =mass×(g-the centrifugal force)
    Hence the weight of the body will decrease when rotation increases.