Range to define emotions
The final range of emotion is completely arbitrary. No matter the interval [a, b], you can adjust the emotions to fit inside. [-100, 100] is perfectly reasonable and is common. An example of use is from GDELT, which provides this interval for average tone of news documents.

Asking if equally distancing the emotions is statistically correct does not make sense. This entirely depends on your use case and opinions. Also, there is absolutely no reason why you can't use negative numbers in a weighted average. 

If you mentioned what you are doing and how you are evaluating emotion, there might be more to say.