Just a bit of clarification. It is not the size of an object that determines its gravity; the object's mass determines the force of its gravity.
Presently it is believed that there are four fundamental forces in nature. Here they are in order of strongest to weakest:
The strong interaction (binds particle in the atom)
The electromagnetic force (electrical attraction and magnets)
The weak force (radioactive decay)
The gravitational force (gravity)
As you see, gravity is the weakest of all the fundamental forces. It seems so great because it is easiest for us to perceive, it acts at great distances, and it works with all masses. Nonetheless, a magnet is, by nature, much stronger than gravity.