I truly believe there is something spiritual about the time around 3am.
When I go back home and sit chatting to my mom in the evening, our conversations always get a lot deeper and more spiritual around the 2.30/3am mark (we can talk all night!) and I have a much higher physic awareness around that time too, I've had clairvoyant experiences around that time and a higher awareness of my astral body.
Also, My nan passed away just after 3am recently and i have heard that it is quite a common time for people to pass over to the other world. (I'm not saying your going to die! I'm just saying that its an easier time to pass over if it's going to happen!)
It really is like the veil between worlds open's at 2.30am and closes at 4.30am!, perhaps it's because the physical area is still and quiet around 3am, so there isn't as much electrical interference and which makes it easier for 'other worldly' beings to step over to ours....
I think you're waking up because you're sensitive to the energy that is suddenly present around you at that time. Think of it like... somebody opened a window and you can feel the cold air coming in so you wake up.