No, because the Earth is more massive than the Moon, Earth has more gravity. Gravitational pull effects the weight of the object. The Moon's gravity is 1/6x (one-sixth) the gravity of earth. So, an object on Earth will have 1/6x the weight if it was on the Moon.
Example: An object on Earth weighing 60 pounds will weigh 10 pounds on the Moon. [60lbs. / 6 = 10lbs.]