In a letter, Jane Austen, herself, apparently called Pride and Prejudice "too light, and bright, and sparkling." However, that was when the book was still incomplete, and I would most certainly argue that book is not "light, bright, and sparkling."
A light novel will lack deep themes. It is only read for enjoyment, like a cheap romance novel. Romance novels are generally character driven, and generally lack deep themes. Pride and Prejudice investigates the moral question of the virtues of pride. It shows how easily one can be prejudiced by another person's influence, even if one is free-spirited and independently minded. It also investigates the consequences of imprudent behavior and impropriety. Finally, it also investigates just how much influence money has on our decisions. While none of these may be earth shattering revelations, she discusses them with an honesty and purity that makes her ideas enlightening.
I would also argue, that while the novel is not full of the dark emotions, like horror, that other Romantic novels are full of, I would hesitate to call it bright. While it does leave you with overjoyed feelings, it does deal with darker questions of morality. In particular, it deals with the consequences of impropriety, especially with respect to Lydia's behavior.