if a large unbalanced force is applied to a stationary low-mass object, what will happen to the objects motion?

The lighter body will start to to move tow time faster in the direction of applied force by the heavier object.

For example if

V1, and m1 is the velocity and mass of the heavier object before collision and m2, V2=0 is the mass and velocity of lighter object before collision

After collision velocity of object 2 will be

V2' = 2V1