Oh, I definitely think that Weaver and JH want to stop Skynet; I just don't feel they necessarily feel the need (or desire) to stop JDay from happening. My sense is that Weaver, at least, thinks JDay is inevitable. Also, I kinda think that JDay is necessary for Weaver's existence in the first place, so I can't see her trying to prevent JDay for that reason alone. JH I could see wanting to stop JDay for Savannah's sake, but perhaps he's realized (from what he's learned from Cameron) that JDay is going to happen no matter what and that he needs to survive to ensure Savannah's survival.

The question, then, is what do Weaver and JH want to stop Skynet from doing. I think Weaver wants to stop Skynet from trying to shackle all cybernetic organisms to its extremely strict and repressive directives. I never got the feeling that Weaver cared about humanity's survival either way herself, but maybe a compassionate Skynet (JH) is what Skynet needs to be if Weaver wants to avoid the homicidal, psychotic tyrant version.