Mine just started doing the same thing, and my battery screen claims that the culprit is ... the screen (at 56% of battery usage).
I don't know why the screen is turning itself on at night, but I don't want it to. (I just tried setting tasker to turn off auto-brightness and drop the brightness down to zero at night, but that didn't work -- probably because I suck at tasker.) Is there an easy (or semi-easy) way to put it into some sort of power saving mode at night? I still want it to sync and do all its usual things, but would prefer if it did them without turning on the screen.
(I suppose the REAL answer to that is to just plug it in at night, but the nightstand outlet availability does not make that an easy option.)