If it’s weather data you’re showing, then I’d be tempted to extract a minimal set of OSM data you need (coastlines, countries, major cities, perhaps major roads) and render a set of tiles yourself based on that. That way you’re not dependant on a third party with which you have no SLA. The other option is to talk to one of the many OSM-based data providers; I’m guessing some of them will have an appropriate layer (and at your usage it might be free).
