Weighted sum of word vectors for document similarity
Yes, your method is valid and it has been studied before it is known as Mean of Word Embeddings (MOWE) or Sum of Word Embeddings (SOWE), although your method is more a weighted mean of vectors. I think that a good starting point for knowing more about the academics of the method is this paper: How Well Sentence Embeddings Capture Meaning. It discusses your method and give some pointers to other papers that also discuss the validity of the method.