Well-acquainted professor does not respond when I share my work?
If you want a reference then you should send an email specifically asking for a reference.  Send it now, there is no point in waiting.  

This doesn't really have anything to do with his response or non-response to your previous email, but if you like you could include a postscript: "By the way, I was wondering if you had a chance to look at the paper draft I sent recently?  If you have any comments I would be glad to hear them."

Two emails in a summer is certainly not a "burden", so forget about that.

Visiting the professor's office would also be fine, except that since it is summer he is not so likely to be there.