Question

Earth gravity is constant?

Answer 1

yes gravity is constant. .....

Answer 2

Gravity or gravitation : if you learnt it , gravitation is a force which is directly proportional to product of mass and inversely proportional to square of minimum separation between them .
  e.g  if  m₁ and m₂ two bodies separated r distance then 
 gravitational force = Gm₁m₂/r²
 
in the case of earth, 
 gravity is a phenomenon of the earth  by which it attracts any body toward its centre . with acceleration g = Gm/r², e.g gravity is constant. but this is true only when, a body located on the surface of earth .but when the body is above or below from the surface of earth acceleration, varies, so gravity varies and graviton field varies. 
hence gravity varies. it will be weak when we go far from the earth surface. 
 
    you can see in the figure how gravitational field varies.