In The Grapes of Wrath, why is there an overabundance of references to eyes?

There are certainly lots of references to eyes in the story. Through the eyes of his characters, Steinbeck shows us the experiences of working-class Americans during the Dust Bowl era of the 1930s. 
The eyes in the story speak of human suffering, anxiety, and grief during one of the worst economic depressions of the 20th century. The dust storms caused many tenant farmers to lose their livelihoods and to make the dangerous journey west to look for work.
In Chapter Five, the landowners kick the tenant farmers off the land they've always farmed. Some of the landowners are apologetic about doing this, but others are matter-of-fact about their hard task. This second group of landowners have little sympathy for the plight of their impoverished tenants. Their main concern is their own survival in light of the extreme drought conditions. The text tells us that the "corn-headed children, with wide eyes" watch silently as the landowners talk to their fathers. The wide eyes of the children symbolize the innocence of youth, an innocence that will be destroyed by the hardships ahead.
In Chapter Seventeen, we begin to understand the toll the journey west takes on the migrant farmers. The men's eyes watch the tires and the roads; the men whose minds "had been bound with acres" must now turn their attention to broken gears, dusty roads, gasoline, and the miles ahead. Through the eyes of these men, we see how the working poor have only exchanged one set of worries for another.
In Chapter Seven, the "intent eyes" of used-car salesmen watch the faces of customers' wives to detect signs of "weaknesses." If a customer's wife indicates interest in a car in her expressions, the salesman works hard to get as much money as he can from her husband. The salesmen are predatory businessmen; like the landowners, they have little sympathy for the average working-class American fleeing the devastation of once-thriving farms. Here, Steinbeck uses the eye as a symbol of inhumanity and covetousness. 
In Chapter 19, Steinbeck tells us that the migrant men grow bitter from their continued suffering. While the wealthy farmers in California thrive, the migrant men and their families suffer. Because of the surplus labor, the farmers begin to pay the migrants lower wages for the back-breaking work they do. In this chapter, the "sullen eyes" of the migrant men betray the depth of their suffering and anger. They must watch their children starve, helpless to change the conditions their families live in.
Meanwhile, the farmers also watch

"with eyes to read history and to know the great fact: when property accumulates in too few hands it is taken away. And that companion fact: when a majority of the people are hungry and cold they will take by force what they need. And the little screaming fact that sounds through all history: repression works only to strengthen and knit the repressed."

Here, the eyes take in knowledge, but the spirit is unaffected by the suffering the eyes reveal. There is only concern for one's survival in light of that suffering.
So, in the story, the human eye is used to highlight both the suffering of the working-class (migrants) and the selfishness of the privileged (farmers and used-car salesmen).