http://www.bvimarineguide.com/clearance.htmlIf you are a charter yacht and taking fee-paying passengers
aboard whilst in the BVI, you need to buy a Cruising Permit and a National Parks Mooring Permit
. This permit allows you to use any N.P. dive or snorkel mooring buoy in the BVI for your yacht or dinghy (these moorings take yachts up to 60 ft). Yachts visiting the BVI for the first time for the year, will be required to pay an Annual Tonnage fee when clearing Customs. This fee is based on the yacht’s net tonnage. If the vessel is to remain in the BVI for more than one month, there is a fee of $200 to temporarily import the yacht for up to one year.
I couldn't find anything listing the fees you would need to pay, or what the annual tonnage fee is, but looks like you are off the hook on the cruising and parks permits as long as you don't intend to use the parks buoys, at the Dogs or Baths for example. Same for the temporary import fee as long as you don't overstay your intended 3 weeks.