The Earth has a mass of 5.97 times 10^24 kilograms. Because weight is defined as the gravitational force exerted on one body by another, the Earth cannot be heavy.
If the Earth was placed on a planetary body large enough to hold it, its weight would be dependent on the constant of acceleration intrinsic to that body, according to Newton's Law of Gravitational Attraction. Multiplying the Earth's mass by the gravitational constant would return the Earth's weight. The more massive the host body, the greater the value of the gravitational constant, and thus the heavier the Earth. The Earth does not have an intrinsic weight independent of a host, but Earth does have a mass.