The roof structure usually drives the biggest cost jump.
Covered deck pricing climbs with added framing, posts, beam sizing, roof sheathing and roofing, the way the cover ties into the house wall, the flashing and drainage detail that protects the connection, and the ceiling and lighting work below. Each of those is a real labor and material line — and skipping one is how covered decks end up with rot at the house wall a few years in.