Depending on the market their may be fees but they would be the same for the owner and the person renting. For example some islands in Hawaii charges TOT (transient occupancy taxes). Some resorts charge for parking.
In general if you rent out more than 14 days in the same county, the owner should be paying taxes to the county. If you are only renting out a week or two this wouldn't apply but since most Airbnb participants are home rentals in the same location, Airbnb has been forced to collect the taxes to make sure the owners pay. Even if the timeshare owner only rents one in each location, I don't think they can get a waiver when using Airbnb. Airbnb also adds their own set of fees. These fees would not necessarily apply if you were renting directly from the owner through a site like tug or redweek or craigslist.