Getting multiple hits to files after enabling BLOB cache

SharePoint Blob Cache is capable of responding to partial content requests.
For large file size client application like media player can decide to send partial requests to server(you ca see requests with status code 206 in IIS logs). SharePoint Server ignores partial content requests and responds to these requests with the entire file , if blob cache is disabled.

So quite possible you get these multiple requests for large files , which were earlier being sent to browser in single request, but since now you have blob cache support , they are divided in to chunk requests.