The fact that the Earth is spinning has no effect on its own mass.
The phenomena of weight requires there to be another object to which the Earth is attracted
towards. Strictly speaking we cannot talk about the WEIGHT of the Earth, only its
MASS.
However a body placed on the surface of the Earth will have weight due to the
gravitational attraction of the Earth. If the Earth is spinning there will be a tendency for this object to
fly off the surface in a tangential straight line. Some of the gravitational pull of the Earth will be
required to produce a centripetal force on the object to keep it moving in a circle with the Earth as
the Earth spins. This means that its effective weight is slightly less than if the earth were not
spinning.
So if the earth stopped spinning the measured weight of a body would increase
– but ever so slightly!
You can observe an effect similar to this by considering what will
happen to the weight of a body as it is moved from the equator to the poles. Its weight would
increase slightly since the radius of the circle in which it is rotating is decreasing. (This is true even
if the non-spherical nature of the earth is ignored).
If the Earth did not spin there would be no change from day to night, there would be sunrises or sunsets!