[note this is an extremely common question already answered: Why do two bodies of different masses fall at the same rate (in the absence of air resistance)?]
The inertia of an object is constant as long as its mass is constant. so the inertia is never overcome, it just stays the same for all times for our puroposes and
while the inertia of the heavier object is greater than the inertia of the lighter object, as you said, the gravitational force is proportionally greater such that both objects have the same acceleration (and thus same position with respect to time if they both are at initially at rest) as provided by Newton's law of gravitation. This requires vacuum and that the objects are aligned at the same radial distance from the body that is attracting them.
It also requires that we neglect the gravitational forces between the two objects compared to the gravitational force between each object and the earth. (as well as neglecting any other forces etc.
note, this is really quite elementary:
newtons law of gravitation says:
$ \vec {F} = \frac{GMm}{r^2}{\hat{r}}$ where $\hat{r}$ is a line radially connecting the 2 bodies
note that if M is the mass of the earth the force vector will be greater if little m is also greater as in the example above
