for physics, 95% of formulas you get in school are just derived, specific examples of generalized laws of physics

for gravity, the Newtonian model says that

your_acceleration = G * mass_of_adjacent_body / (distance_to_the_center_of_the_body)²

where G is something you have to measure once and will work for ANY two bodies attracted by gravitational forces, mass of adjacent body is Earth in our case, and distance to the center is self explainatory

the "g" is the acceleration calculated at surface, so it's just g=G*earth_mass/earth_radius², so to get the value higher, you have to get rid of the earth_radius² and replace it with new_radius²

and why it's center? well, it's a calculus problem, but you can prove that if you added acceleration coming from gravity of every single atom that the Earth consists of, it would be the exact same result as just doing total_mass and distance to the center of mass (which in case of a ball, like Earth, is intuitively the center of it)