Most remodeling and cleanout debris loads without trouble. The limits come from the state authority's rules and from what the city itself refuses at the curb.
Hazardous material is out of a standard container everywhere: paint, solvents, fuel, used oil, antifreeze, pesticides, pool chemicals, pressurized cylinders, and anything corrosive. Liquids and medical waste cannot go in either. The city's own code bars radioactive waste, acids, caustics, explosives, and toxic gases from collection, along with anything the Delaware Solid Waste Authority treats as hazardous.
Tires are kept out of city collection entirely and are billed by weight at the state landfill, so they belong in their own arrangement. Electronics, batteries, used oil, and latex paint all have free state drop-off programs, which is the cheaper route by a wide margin.
Asbestos is the one item Delaware handles differently from most states. The authority does accept it at Cherry Island, but only under its own written procedure and with a waste shipment record, and it is billed per ton plus a charge per load. Never put it in a general debris container.
The city also will not take remodeling debris at the curb beyond a few pounds from minor repairs, nor single items over 40 pounds or four feet long, nor limbs six inches or more across. That is exactly the gap a roll-off fills. If you're unsure about an item, ask your account manager before it goes in.