Question

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

Answer 1

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

Answer 2

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. ”