I almost considered asking this question on WorldBuilding, however I wanted the brute mathematics on the subject, so please excuse the theoretical nature of this question.
I understand the basic nature of gravity wells, in that they are analogous to literal wells in the fabric of space. I also understand how bigger bodies in space have larger gravity wells, how big would that gravity well have to be to dominate the gravitational attraction of objects within it's well? How big would it need to be to give a object exit velocity from a planetary body? I understand that the gravity well and the planetary body would attract, but is it possible to move objects away from larger gravity wells with a smaller, but closer gravity well? My thoughts are that if you are close enough to the well, you would receive much more attraction than if you were farther away. Is this correct?
While an apple does have gravitational attraction, you do not feel any noticeable pull from the apple. What's the minimum size that a body must be for you to notice gravitational pull? What if the hill spheres were aligned in such a way that merely jumping would allow you to change gravitational sphere, à la Mario Galaxy?
In my crude drawing I've illustrated my theoretical situation. The object (the dwarf) is close enough to the moon to be within its dominant gravitational pull, and is therefore being pulled away from Earth.
John Rennie pointed out the concept of Hill spheres in a comment, which might be useful in trying to figure out if they could be used to dominate nearby objects.