For the most part, the costs of recycling are economic rather than environmental. There are a few environmental costs. These would include the fuel that powers the trucks that pick up the recycling and those that bring it to places where it will be recycled. The costs also include the energy used to break down the recyclables and make them into something new. All of this energy use damages the environment to some degree.
The economic costs of recycling are more daunting. They include the cost of the labor for picking up the materials, sorting them, bringing them to a factory, and then recycling them. They also include the monetary costs of the energy used to recycle the materials. These costs are often higher than the price that can be gotten for the recycled materials.