This is a difficult question because Whitey narrates the story of Jim, with whom it is impossible to have sympathy, while saying repeatedly what a great amusing and entertaining guy Jim is. By virtue of association, we are put off from sympathizing with Whitey as we come to understand Jim. In other words, how can we possibly sympathize with someone who has a high opinion of a man like Jim? If we look below this surface reaction, will we find a reason to sympathize with Whitey?
First of all, judging by Whitey's speech, he isn't well educated or very intelligent. He is a simple man who got himself trained in a respectable job and does well for himself as a barber. The first paragraph holds a good illustration of his speech:
most of the boys works all day and don't have no leisure to ... get themselves prettied up.
Whitey is a friendly sort of man. Instead of being stand-offish with the newcomer, as some might be, Whitey is very welcoming toward him: "I hope you like it good enough to stay." Similarly, Whitey does have an appreciation for individuals who are actually good, thus can distinguish between good and bad sorts: "It was tough on Julie as the young people round this town--well, she's too good for them."
What seems to trip Whitey up is the fact that Jim's crashness and bullying generally elicit the response of laughter from pals, like Hod. Whitey seems unable to recognize the pain that lies behind "Milt himself would force a smile." Whitey's simple nature seems unable to see situations as they are if there is laughter associated with it:
[Julie] pretty near fell downstairs... they chased her all the way home, hollerin', ... "Oh, Ralphie, dear, is that you?" Jim says he couldn't holler it himself, as he was laughin' too hard.
On the other hand, it seems that Jim's bad actions do have an affect on Whitey after all, even though he may be unable to identify it specifically. Whitey sympathizes with both Julie and with Paul Dickson, who had the brain injury. In the end, we also learn that Whitey does confess that Jim might have brought his end on himself, though the phrasing of his comment creates some ambiguity to his reasoning: "It probably served Jim right, what he got."
In sum, it just may be possible to sympathize with Whitey after all because he does have sympathy and understanding for Julie and Paul Dickson and does see that perhaps--in one way or another--Jim had brought on his own end himself.