Question

A small object placed in the gravitational field of a more massive object will

Answer 1

Two objects allowed to move freely will accelerate toward each other
in response to the gravitational forces between them. 

It doesn't matter whether they have equal masses or vastly different
masses ... each object accelerates toward the other one. 

The less-massive object has greater acceleration, and the more-massive
object has smaller acceleration. 

Yes. When you fall to the Earth, the Earth falls to you, but with less
acceleration because it has less mass than you have.