Taking a look at the SSTs and hurican heat potential (HHC) maps, there isn't a lot of heat before it reaches the Windward Islands. If the storm curves north toward the east coast, the surface temperatures are lower, and development will be slower.
I do see that in addition to lower-than-optimal SSTs ahead of it, there appears to be some SAL (Saharan Air Layer) dipping in front of it that will probably slow it's development.
I would expect that it won't do a lot until it passes the Windward Islands, but then it will get into much warmer waters that could aid development, but that's too far out for anything more than guessing.