Will it be a problem to bike uphill with a rear pannier with books (~2lbs)
Since the weight will be the same, you won't even notice the change in terms of climbing. You will notice that your back will ache less and be less sweaty. Depending on your bike, it may even balance better with the weight lower to the ground. 

Biking up a hill with a few extra pounds won't make much of a difference; you only really notice a difference in climbing or handling when you're carrying groceries or camping equipment or passengers. (Or if your bike is not suited to carrying cargo.)

I suggest you either get two panniers to distribute the weight, or get something like a trunk rack bag so you don't need more than one bag. (You could even get a a basket and toss your existing backpack in it.)

You'll find more general info about the various cargo systems under the cargo tag, or in this article.