Why are the cabin inner windows so flexible? A few days ago I flew on an A321. While pointing to something outside my finger touched the window. It made a crackling sound and felt quit flexible.
I was able to push it at least 5mm without any effort (I didn't wanted to push further because I thought I might break it).

On the way back, I flew on a B737 and the same thing applied on its windows as well.

I'm pretty sure it's that thin because of the weight but is there any other reason for such a thin (and probably fragile) inner glass which could be easily damaged by a passenger by mistake?
The inner window is just a plastic protective cover, so that you don't touch the glass, which is probably very cold at altitude. You'll notice on the inner window there is a tiny hole at the bottom to equalize pressure and prevent condensation. 



See this article that explains it