Heavy copy editing
In addition to cleaning up errors, a heavier copy edit includes scrutiny of a piece of writing’s logical structure, flow, and persuasiveness. If I am doing a heavy edit on your piece, I will offer explanations as well as comments about my corrections. An edit at this level will often include suggestions for moving or eliminating paragraphs (or longer passages); you may want to consider my propositions, counteroffer, and send the rewrite back for a second go-round.
This is the stage at which I address global concerns. Is your writing appropriately engaging? (Or is it condescending, off-puttingly quirky, overly stiff, or simply inelegant?) Does it make its points succinctly? (Or does it ramble, or drag, or wander off topic?) Is your piece optimally organized? Are there points that are hammered too hard, while others need expansion? Does it match the level of expertise of its intended audience?
Occasionally, a heavy copy edit becomes more of a substantive edit; this progression usually happens organically.