This uses the Enviroment.xml file which also controls weather! It SHOULD NOT! Weather is controlled by the maps Environment file!
It's just the way the enviroment.xml works. Sure we could maybe separate it but then we'd have to convince map makers to also split weather separately. Everything just kinda works together in the single file. However you can copy paste your weather settings into relight and it will then use the settings you previously had. Or copy relight into your environment xml ect ect
I think it's possible, you can simply just not include the clouds/weather/season part of the xml and just have it in it's own seperate xml but I'm unsure how to make the map.xml load the now two seperate environment files. The caveat to all of this is that the clouds/weather are responsible for assigning the appropriate cubemaps to the environment. Without it, or the wrong cubemaps will make objects look very out of place.
So what I tried to achieve the split of weather and light: I edited your xml to contain just the lighting data and copied it, along with the other xmls and cubemaps, to folder of Additional Game Settings mod with custom lightings. Now it is easy to turn it on and it seems to work, but I need to try it with maps with nonstandard weather like Rennebu to see if it has the intended effect :)