Because your timeshare is paid off, and it doesn't sound like there are any backdues, transferring or selling the timeshare is one of the options you have. These options could work, but for what you described, I don't think that is what you are looking to do. If you are going to attempt to sell or transfer a timeshare, you will be responsible for all of the dues/maintenance fees until the timeshare is sold/transfered, which you already described as a burden.
It is impossible to guarantee to sell something, so your timeshare could be sitting around for a while, while you continue to be responsible for the fees. Every timeshare company also charges their own unique "transfer fees", some of which run over $1,000. You can see how this can add up: transfer fees, maintenance fees, transfer/listing company fees, etc.
Karen did provide some great information though. Your only hopes in terms of selling it, if you do choose to go down that road, would be to list it for "free" essentially, but you would still be responsible for a chunk of change. Even then, hundreds of timeshares are on eBay right now for less than a dollar, so the chances yours gets picked up is slim.
My recommendation would be to:
1. Call the developer and let them know you no longer have any interest in owning the property and would like to offer it back to them for free by way of a "quit-claim deed". It has a low probability of working, because they already have you locked into the contract, but it's worth a shot as Karen mentioned above.
2. Transfer the timeshare to someone that you know. When you are working with 3rd parties, it becomes a little bit risky/time-consuming, so you want to protect yourself from paying the transfer fees/company fees, then end up still owning the timeshare.
3. Cancel the timeshare with a reputable company. Timeshare cancellation is relatively unknown still, but is slowly becoming the standard to get rid of timeshares. Do your research. Ask questions. This option will probably cost around what the transferring/selling method costs, but is typically faster and guaranteed. Plus, there are companies that are able to cancel your maintenance fees, so it could essentially pay for itself, dependent on what the maintenance fee/cancellation costs are.
Let us know what you find out, and good luck!