I've had this question on my mind for quite some time and saw in an anime again that the characters when not doing much read a thin book.
Does anyone know what this books are because most books are bigger and thicker.
That's actually a pretty common size for Japanese novels (Bunkobon, designed to be compact). This blog entry shows the respective sizes of a Sword Art Online book in Japan, Korea and USA - the standard page size for a Japanese book is about A6, or 105mm × 148mm (4.13in × 5.83in).
The thickness of the book is also not unusual - as you can see here, many Japanese books are quite thin even taking into account their small cover dimensions.
EDIT: And as pointed out in a comment, the paper used is often thinner, and both the font size and compactness of the Japanese language also contribute to the book being thinner than their Western counterparts.