The Nekton is the most single civilized live aboard on the sea. You won't need to bring much!
First- maybe think about what you won't need! All live aboards are different, and you should know that the Nekton provides towels for inside your cabin as well as on deck. You won't need any dive bag other than your travel bag as all of your gear is held in stainless steel bays at your station. Your weight system should be able to accomodate lead shot bags, not hard weights. I'm sure your BC is adjustable to accomodate 90 cf tanks, only 1970's vintage rigs might have a problem.
You might like a small (12x12") mesh goody bag to hold small items that you'll want to carry off the dive deck such as computer, watches, etc. Another such bag to contain the small stuff you leave down on the deck, but not absolutely necessary. One pair of shoes will do. Insect spray (for no see ums) while on shore leave.
Altho there is a wake up call before every dive and meal, maybe you'll want an alarm clock.
On certain itineraries you have to take a commuter plane to Andros, so do some checking with STARS (the booking agent) in regards to weight limits and fees for overages.
They can sell you batteries and a few other things while on board. In the mean time, think about all the stuff you might like on a dive trip and skip a lot of the clothes (there is no dirt!). A light windbreaker/polarfleece and a hat, get going and out the door!
Enjoy the finest ship in the Bahamas! (But be sure to try their Belize cruise in the Caribbean as well!)
Roatan Man