I'm imagining designing a software product around this and presenting it to a C-Level, explaining that we use "PirateWeather" and I think I'm going to get grilled with lots of questions and concerns based on the name alone.
This is a good service and should be "branded" with a better name. Maybe a play on the whole DarkSky name like LightSky or "Sunset" which works exceptionally well since DarkSky was sunset by Apple. Maybe StarrySky, LateSky, NewSky.
I am usually someone who says that names don't matter as much as people think they do, but PirateWeather just seems like a huge hit in the wrong direction. But the product is solid so maybe it can survive despite the name.