Since for objects of the same shape but different weights, at the same speed the net downward force is greater on the heavier than the lighter (as the drag will be equal). At the terminal velocity of the lighter there will still be a net downward force on the heavier and so it will still be accelerating.
Note the form of drag you used (drag proportional and in the opposite direction to speed) is appropriate at small Reynolds' number. In practice this means a small or large surface area object falling in air, or a medium more viscous than air.
This type of result is why Galileo and Aristotle disagree about falling objects. Aristotle's version that heavier objects fall faster then light is obvious from everyday experience. It takes a Galileo to realise why this is not useful and try to decouple drag forces from gravitational.