What does the large stone represent in Shirley Jackson's short story "The Lottery"?

While the picking up of the large stone by Mrs. Delacroix during the stoning of Tess Hutchinson can be interpreted in many ways, let us look at what Helen Nebeker, a critic, writes in her article " 'The Lottery': Symbolic Tour de Force," which was published in American Literature (vol. 46, no. 1) in 1974.

The Delacroix family, whose last name is French for "from the cross," already has a symbolic name which elicits thoughts of martyrdom, such as the one experienced by Jesus on the cross. Ironically, the family  shows none of the signs of goodness that often come with the view of a martyr. In fact, the collective attitude of the Delacroix clan, based on their reaction to the lottery, is that of making martyrs out of others, namely, whoever is picked during the drawing. Proof of this is the fact that they are the first family mentioned in the story that is fully engaged in the process of collecting stones, for what will become a macabre and bloody activity later in the day.

Mrs. Delacroix, a friend of Mrs. Graves, speaks quite candidly to Tess before the lottery starts, during it, and always shows kindness toward everyone. When Tess is finally revealed to be the "winner" of the lottery, the Delacroix children quickly step up to the stoning, as they had been collecting rocks from the start. Mrs. Delacroix, however, picks up a stone so large that she needs both hands to lift it. 

The Lottery--Shirley Jackson

...the pile of stones the boys had made earlier was ready; there were stones on the ground with the blowing scraps of paper that had come out of the box Delacroix selected a stone so large she had to pick it up with both hands and turned to Mrs. Dunbar. "Come on," she said. "Hurry up."

So: Based on the analysis of the Delacroix clan, we can infer a few things. First, that the large stone was picked on purpose by Mrs. Delacroix so that she WOULD NOT be able to hurt Tessie. If she cannot lift it, how can she possibly throw it?

Second, that the large stone is meant to hurt Tessie in the worst way possible because Mrs. Delacroix, like her family, may have psychopathic trends. Weren't they all collecting stones more than avidly from the very beginning?

Third, that the large stone represents duality: Mrs. Delacroix follows and obeys the status quo of the village by participating in the lottery. However, she really does not intend to fully participate and makes herself almost unable to carry the stone. This may show a fragment of humanity still left in her character. 

Therefore, the large stone represents doubt. When one is sure to do something, and do it well, one does not use the hardest or more difficult tools to accomplish a mission...unless one is not fully sure on whether that mission should be accomplished or not.