In chapter 3, when Candy finally gives in and allows Carlson to take his dog and put him out of his misery, why doesn't Candy look at his dog before Carlson takes him?

Candy is an old swamper with bent shoulders, who knows his days of being a useful ranch hand are coming to end. He has an old sheepdog he is very attached to that he has owned since it was a pup. It is graying, like Candy, and it is blind and has trouble walking. Candy, however, remembers how it used to be, saying, "God, he was a good sheepdog when he was younger."
Carlton, another ranch hand, wants to shoot the dog because it sleeps in the bunkhouse with the men, and Carlton finds it a nuisance:

That dog of Candy’s is so God damn old he can’t hardly walk. Stinks like hell, too. Ever’ time he comes into the bunk house I can smell him for two, three days. Why’n’t you get Candy to shoot his old dog and give him one of the pups to raise up? I can smell that dog a mile away. Got no teeth, damn near blind, can’t eat.

Carlton tries to persuade Candy to shoot the dog, saying it would be putting it out of its misery. Slim also joins in, telling Candy he should end the dog's life, arguing that he would want someone to shoot him if he got so old and infirm. However, Candy is unwilling to shoot the dog, saying he doesn't mind taking care of him. He explains that the dog has been with him a very long time.
Finally, however, Candy feels he has no choice but to give in to the pressure. He lets Carlton take the dog out and shoot him:

At last Candy said softly and hopelessly, “Awright—take ‘im.” He did not look down at the dog at all. He lay back on his bunk and crossed his arms behind his head and stared at the ceiling.

Candy doesn't look because he loves the dog, doesn't want it to die, and feels he is betraying a friend by allowing Carlton to shoot it. He also identifies strongly with the dog. Candy is old too, and knows that, just like his dog, he won't be wanted once he can't work anymore. Candy is now alone: the lives of the seasonal ranch hands are lonely because they have to follow the jobs and can't put down roots. Candy has lost his one faithful companion.
Candy's loss of his dog and the emotional pain he feels over it foreshadows George's eventual loss of Lennie.