I tried to sell the Elder Scroll to Urag gro-Shub and was unsuccessful. Now I have been trying to get rid of these damn things for a while. They are way too heavy. Do I have to fight the dragon before I can get rid of them?
The Elder Scrolls are Quest items, therefor can't be sold until ALL related quests are completed. So you got to check if the following quests are done:
And if Dawnguard is installed:
Also because it is a quest item it won't weigh anything: Do quest items weigh anything? as stated you can try it out by placing everything you own in a chest and check your weight.