If Earth’s mass were to double, all gravitational relations, including potentials, would also increased but it’s not exactly double as the equation should also account for the other body or bodies masses.
I think the simple Newtonian version is: Break down each gravitational relation (A and B pull on each other) in it’s components: A pulls on B, and B pulls on A. If you double the mass of A, this has two effects:
A pulls on B twice as much
B pulls on A the same, but needs twice as much force to achieve the same acceleration (a = F / m)