Is know as a force that pulls an object weight to center of the earth

That force would be gravity.  Gravity is what pulls any object down towards Earth due to the large mass of the Earth.

Gravity. More info on gravity from Wikipedia: “Gravity (from Latin gravitas, meaning 'weight'), or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or gravitate toward) one another. ”