Sorry, can you clarify? You appear to be claiming that a body's inertial mass and inertial resistance changes when under different levels of gravity.

Can you clarify this? Why is the inertial force of a bullet or bowling ball approaching you the same in weightless space and on Earth? According to that logic inertial resistance should disappear in a weightless environment far from gravitational fields.

If a bowling ball is in vertical free fall towards the surface of Saturn, are you claiming that it would take more force to move it sideways horizontally during its downwards descent than on Earth, since the bowling ball now has a greater inertial mass? And if not, why should the force to move that object sideways horizontally be the same as on Earth or in weightless space?

Sorry, perhaps I've expressed it poorly but I am not claiming that a body's mass changes. It stays the same.

F = m*a. F is the force applied to a body, m its mass and a its acceleration. From that, you can see that a = F/m, that is that the acceleration of a body is proportional to the force applied to it divided by its mass.

Suppose we have an object A and a two times heavier object B. The same force will accelerate B less (by a half) because it has two times greater mass. Alternatively, a two times greater force has to be applied to B if you want both objects to accelerate the same way. So far so good?

Now, let's take the Newton's law of gravity F_g = k*m*M/r^2. F_g is the gravitational force, k is a constant, m and M are masses of two bodies and r is the distance between them. If the distance increases the gravitational force decreases. If one (or both) of the masses increases the gravitational force increases too.

Let's return to objects A and B and let's drop them on the Earth's surface. Object A has a mass m and is accelerated towards the Earth by gravitational force F, so it achieves acceleration a. Object B has a mass 2m so it's two times harder to accelerate. At the same time, object B has mass 2m so the gravitational force between object B and the Earth is 2F. It's two times harder to accelerate object B but the force accelerating it towards the Earth is two times greater as well. So, 2F/2m = F/m = the same acceleration a towards the Earth. In conclusion, A and B are accelerated identically towards the Earth.

Now, let's take objects A and B to Saturn and drop them there. Object A has the same mass m but Saturn's mass is much greater than Earth's mass. So, the gravitational force is greater, not because object A's mass m would be different but because the planet's mass M is greater. So on Saturn, object A achieves much larger gravitational acceleration a (or g) than on Earth. Nevertheless, the same that applied to the relation between objects A and B on Earth applies on Saturn. Object B still has the same mass 2m so it's still two times harder to accelerate. At the same time, object B still has the same mass 2m so the gravitational force between object B and Satrun is again twice greater. It's two times harder to accelerate object B but the force accelerating it towards Saturn's core is two times greater as well. In conclusion, A and B are accelerated identically even when on Saturn.

The same goes for any planet/star/whatever. Bodies with different mass are harder (or easier) to accelerate but at the same time the gravitational force between a body and the planet/star/... is greater(/smaller). So in conclusion, all the bodies on the same planet/star/... are acceleratde the same way, none, every has the same acceleration g. However, the particular value of acceleration depends on the mass of the planet/star/... so different planets/stars/... have different gs, different values of acceleration of bodies on their surface.

Is it clearer now?