Here is a Live Web Cam from St-Barth that is just West of Barbuda. You can see the wind is certainly picking up.
https://www.youtube.com/watch?v=hG-GpHPkBoM
I’ve been watching the live cam at St-Barth you posted. The storm is on top of it now and the power just got knocked out.
Well, it came back on as I typed. Don’t know if it will stay on though. They’re having a terrible night there. :-(