Rest assured, Negril is no being bothered by seaweed. I called Royalton, Boardwalk Village Resort, Charela Inn and Travellers and they are taken back that someone would compare the situation in Belize, which gets the direct eastern Atlantic current hitting their beaches, while the Negril beach is protected by the Western prevailing currents that block the seaweed.
My advice is to skip the seaweed in Belize and enjoy the seaweed free beaches of beautiful Negril!