Since the acceleration is always `a =F/m` and the dependence of speed on constant accelerations is of the type `v=a*t =(F/m)*t` it means that when saying "an object is moving with a speed proportional to the force on it" both persons are right.
However the constant of proportionality between speed and force is time, which basically means for an uniform increasing speed, a constant applied force.
This means that the arguments of Heather are valid and the arguments of Kasi are false. In reality, both students are right, the force is essentially constant but at the same time is increasing when the object is approaching Earth ("essentially" is the main word here).
But at this point the reasoning of Kasi begins to fail. First the velocity does not get larger because the force becomes much larger, but because time passes (as shown above the constant of proportionality between speed and force is time). Second, since the acceleration is proportional to the applied force (`a =F/m`) it is false to say that the acceleration is constant and the force gets larger at a constant rate. (Otherwise said, the time is not involved in the definition of acceleration, therefore to relate the rate of force change to the acceleration is a nonsense).
The acceleration is constant basically because the gravitational force expression is
`F = G*(m*M)/R^2 =m*g`
where `R =6371 km =6371000 m` and a difference in the value of `R` of 10 meters or so does not change significantly the value force.
Thus the argument that is invalid here is that the acceleration is constant due to the constant rate of change in the force.