I’ve read a couple of different posts and even in a couple of books recently about people “pouring over” documents or books. 

I wondered at first if this was one of those things Americans do with words that nobody else does, but I checked, and it’s not. It’s simply an error caused by confusion by words that sound the same even though they are spelt differently and mean completely different things. 

What the people in question should be doing is poring over their books. 
To pore over books or documents is to be completely absorbed in what one is reading or studying. It suggests thoughtful application and concentration. 
The gerund is poring. 

To pour over books is just going to make a mess, and probably ruin them completely.  It’s really not advisable.