Cronus' weakness was his fear of being overthrown by his own children. In the end, this weakness was his downfall.. but I'll go into more detail as this is a very interesting story!
Who was Cronus?
Cronus was, in Greek mythology, the leader of the first generation of Titans. He came to power when he overthrew his own father, and ruled until he himself was overthrown by his own son, Zeus.
What was Cronus' weakness?
Cronus was very paranoid, and always feared that he would be overthrown by his own children, in much the same manner that he overthrew his own father.
This fear led Cronus to commit the awful act of eating his own children upon birth. Zeus was the only child to escape this terrible fate, and would later overthrow Cronus and restore normality to the world.
As you can see, Cronus' main weakness was his fear of being overthrown, which ironically enough, led to him to actually being overthrown later on by Zeus.