Mapbox maps require the use of Mapsbox’s own mapping engine, which conflicts with the mapping engine that our plugin is based on (Leaflet). On top of that, the new Mapbox maps are vector maps, whereas Maps Marker Pro uses raster maps. We therefore don’t have any plans to support the new Mapbox Studio maps at this time. You can continue to use the classic styles for as long as Mapbox provides them, even in Version 4, by adding them as a custom layer.
Maps Marker Pro allows you to use all kinds of maps which are available via WMTS or WMS standard. Those custom layers can be added via Settings / Layers / Custom:
A community curated list of custom layers an be found at https://mapsmarker.com/custom-layers
For dedicated weather layers, please have a look at https://gis.stackexchange.com/questions/6345/listing-available-online-wms-services-weather-land-data-place-names for a starting point – many of those may be configured to be used in Maps Marker Pro too.