What does the dog represent?

I see the movie broken up into a chronology of four chapters depicting life: childhood, in which we receive indoctrination; young adulthood, in which we question our indoctrination and assert our identities; middle-age, in which we doubt our identities and assert our existence; and end of life, in which we confront the meaning of it all.

I think the weiner dog is there as a sort of pun on the axiom that "life is nasty, brutal and short". Soldonz is saying that, despite his cynicism and pessimism, life - like the adorable weiner dog - can be sweet and long, despite being "a dog's life", as it were.

The dog represents religion.

The dogs are nothing more than props, fetishes, something that people own to feel better, pure futility (for Solondz), so they're just the device for a story about the meaninglessness of life. Apparently a lot of people care about dogs dying in movies and as the director likes to tease the audience too much, he does just that (the first dog didn't die, so we're supposed to feel good about that, but then he kills the other two, he's relativizing, like if he says dogs can live and die and whatever to that). See, when Dawn find her happiness on Brandon she just doesn't care that much about the dog.

A few ramarks with spoilers.

The dog is "born" looking at the sky from a cage.

1. The first family doesn't love him or care about him. We see this mostly from the fact that they don't give the dog a name, they call it "weiner dog".

2. Dawn names him "doo dee" or something, which means *beep* an american slang I guess that I never heard before.
I think she also doesn't care about the dog and the only reason she saved him is that she snaps. She was autistic, she choose to drive with a guy who does heroin, with no prospect of future. She abandons the dog with no regrets. She is the same autistic person that she was in "Welcome to the dollhouse".

3. Professor Smitsz doesn't care about the dog either. We don't see him petting the dog, not even feeding or anything. I think he got the dog just for company and to walk him so he can exercice. We then see that he leaves the dog with a bomb planted, showing that he doesn't give a beep about the dog.

4. The dog is now named "cancer". What more can you get. We don't see the owner showing any feelings towards the dog, except at the end after she has that dream about dying. Then she calls the dog but it is too late because the dog is running towards his death.

I think that the dog lives a choiceless life, exactly how we see the old lady saying in the dream "but I didn't choose".

The boy from the first part didn't choose to have cancer or to be depressed.
Dawn didn't choose to be autistic.
Smitsz didn't choose to be a pesimistic lonely guy who would snap at one point.
The old lady said that she didn't choose.

And the dog didn't choose anything except the end when he run towards his death but I think that even that was not a choice.

Wiener dog's heart is a lonely hunter.

Sometimes I go about in pity for myself, and all the while, a great wind carries me across the sky.