[gluckmeea]

Seems like the 'real' skynet is trying to kill John Henry who seems to be a AI built to counter Skynet on judgement day. (Reasoning, the other side has direct control of 'metal' that hasn't been aligned with Conner) The only problem with this theory is Skynet went self aware and then let off nukes in self defence, to attack John Henry Skynet would have to be selfaware now.
Thinking on events of the past, Conner might have sent Weaver back to get the experimental AI and develop it so it valued Human life, otherwise she'd have just carried a copy of Skynet's oringal code. So in my eyes, Weaver's efforts have been leading towards building something that doesn't exsist in the future a true AI that is sympathetic to Human kind. I don't know if they could use it to replace Skynet, but they could use it to defeat Skynet before it got control of the US nuclear arsenal.

Did anyone else get that impression?

Or she could be trying to make a new kind of terminator that can easily pass as a human and infiltrate the rebellion.