You have been given good advice above.
Some people may be uneasy with the whole transfer process which could be a reason why they are willing to pay some entity thousands of dollars. No reason to make that a concern as there are transfer companies that will handle everything for you for a nominal fee. One such company is LT Transfers which has been recommended on TUG (disclaimer - I have never used them but they have gotten good reviews from those that have used them).
I looked at eBay for sold Berkshire timeshares. There are a handful. Sold prices ranged from one cent to $25. A common theme for them were free closing and transfer. Most had an included gift card ranging from $250 to $400. My recommendation? Offer it for free on TUG and elsewhere with closing and transfer fees paid. Include an incentive to also pay 2019 maintenance fees, and maybe even 2020 fees. Another option, offer it free with closing and transfer fees included and a $1,000 gift card. I would bet that it would sell and you would have probably still saved at least $1,000, maybe even more, than what Wesley is going to charge you.
If you post an ad please do more than "I want to get rid of this timeshare". Include things that make the resort great - close to shopping, pool, resort activities, local attractions, WIFI, fitness center, laundry facilities, family oriented, free DVDs to rent, day use, etc... Include personal stories of any great vacations that you had with your family. Include photos of the resort. In short, sell what you are offering and make it stand out from all of the other similar ads! Doing these things won't guarantee a sale but it will certainly help your chances.
One last thing, please do not pay a timeshare listing company a dime for them to "advertise" your timeshare. They will purposely mislead you as to the value of your timeshare. They want you to think that it will sell on their website for thousands of dollars. All lies. They want you to believe this because they will charge you upfront $750 or more just to have the ad on their site. If they told you the truth as to the value then they know you wouldn't pay them anything. Once they have your money they could care less if it sells, after all they already got paid. You will be out $750+ and still have your timeshare to sell.
Good luck!