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.