no Shape keys and weight painting, are they compatible? I've made a shape key for blinking, but the head is also weight painted 100% to the head bone. When the head is not attached to a skeleton, the blinking works fine and I can control it via a script in Unity 3D. When the head is weight painted, the eyes stay wide open. 

I'm assuming that the head bone is telling those vertices to stay in place and this must be overriding the shade key. Is that right? 

Is there any way shape keys and weight painting can work together? 

*I should add that this is only a problem when the character is being animated. I'm not sure how to get around this as I can't exactly not animate the head. I'm stuck.
You need to export the FBX file using the ASCII exporter, not the binary one. 

My character can now blink while being animated. The only issue is that the ASCII exporter exports the model x100 smaller. This can be easily changed in the model properties panel, but if there is a way to import it with the correct scale that would be great.