Depends on what you want to believe about humanity. If you want Mrs. D to act in the same cruel, unhumane, traditional method as everybody else, then she is picking up that large stone in order to get this year's lottery done with in a hurry. She'd be picking up the largest stone she can still throw because that's what you're supposed to do on lottery day.
If, however, you want to believe that everyone has some smidge of decency somewhere inside, then she is picking up a stone that's way too large to travel to her "target". She could be seen by other townspeople as an able and eager participant in this year's stoning while still maintaining some personal shred of morality in knowing that she really had no part of killing Tessie.
The great part about reading a story, is that you get to choose why she did what she did!
Mrs. Delacroix (of the cross) does not refuse to throw stones; however, she can refuse to hit the mark.
She picks a large stone because she doesn't actually want to hit her friend. One can throw a small stone quite a distance, but a large one...falls not far from the thrower.
It does seem terribly incongruous for Mrs. Delacroix, who seems the epitome of civility and sweetness, to attempt to hurl a stone so large she can scarcely lift it. Some critics claim that this action is symbolic of the duality that exists in mankind. People have the potential to be both kind and cruel, and behind the civilized facade that people present each day hides the underlying truth of the savagery that exists within us all.