When you halve the mass of an object, the acceleration doubles, assuming the net force acting on the object remains constant.

This is directly related to Newton's Second Law of Motion:

Force (F) = Mass (m) * Acceleration (a)

* If the force is constant: As you decrease the mass, the acceleration must increase to maintain the equality.

Example:

Imagine pushing a box with a certain force. If you replace the box with one that has half the mass, you'll find that it accelerates twice as fast because the same force is now acting on a smaller mass.