There were, I would argue, two major impacts of these wars on China's economy and society.
First, the wars led to an increase in opium use in China. According to one book I use as a teaching resource, the amount of opium being imported into China in the 1850s was double the amount being imported in the 1830s (East Asia: Tradition and Transformation. Fairbank, Reischauer and Craig). This had an impact on Chinese society and economy as more people became dependent on the drug.
Second, the increase in foreign contact with the Chinese led to major changes in Canton, where the contact was most intense. This led to a major increase in the amount of business being done by Chinese. It also is said to have helped lead to Chinese nationalism and a desire to overthrow the Manchu because the Chinese saw the way the westerners showed patriotism and nationalism, and they wanted to copy that example.
These are some of the major impacts of the wars on China's economy and society.