I think we have enough balloon questionsballoon questions already to say that balloons in general are on topic here, so the question is if there any reason why weather balloons specifically should not be. IMO, if the question is about the balloon itself or how to operate it then yes, it's on topic; if it's about the mission or the activity that the balloon supports then the answer is (generally) no, unless that mission is clearly aviation-related itself.
Questions about constructing, operating or navigating the balloon would be on topic, unless perhaps you ask about generic gas/buoyancy calculations that are not specific to aviation. Questions about meteorology instrumentation, data processing or other aspects of the balloon's mission would be off topic.
There's a possible grey area here, because weather balloons and weather in general are very important and relevant to aviation so arguably the mission could also be aviation-related in some scenarios. But I think that's the same with most things and individual questions can always be voted on or off topic, whatever we think about the subject in general.
Perhaps a clearer example would be a hot air balloon used for safari tourists in Africa. Questions about constructing, launching, navigating, retrieving and generally operating the balloon itself would be on topic. Questions about what animals to look for, good game areas to launch in, how much to tip your pilot, the ethics of photo safaris vs. shooting safaris etc. would all be off topic.
But as always on StackExchange, if in doubt just post your question and see what the response is.