Why does it appear that an object with less mass falls toward an object with greater mass?

An object with greater mass exerts more gravitational force than the object with lesser mass; so,an object with less mass falls toward an object with greater mass.

Explanation:

Newton's second law of motion defines the inverse relationship between mass and acceleration.

.........................(1)

Consider mass

Objects with more mass have more gravity. An object with greater mass exerts greater gravitational force than the object with less mass.

....................(2)

Where G= Gravitational constant

F= Force of Gravity

m₁,m₂ = Mass of objects

r= Distance between the two objects

From (1)

Equating (1) and (2)

Gravitational acceleration:

Gravitational acceleration (g) on the other hand is independent of the individual objects' mass. It is related only to the mass of the object creating gravity, the one with higher mass(m₂).

This makes the object with lesser mass fall towards an object with greater mass. Even though they experience the same gravitational acceleration, the gravitational force depends upon its mass.  

it will increase due to the time span