Well-acquainted professor does not respond when I share my work? I'm a master student in statistics. I took this professor's class, in which I've done very well. I have discussed with him about my research project a few times while taking the class, although he is not my thesis supervisor. It's been 2,3 months since my last time meeting him. I shared my paper draft (written over this summer) with him recently via email since he seemed genuinely interested in my progress and even suggested I should keep him posted. I'd also like to ask him for a reference in the fall for PhD application. The draft was quite lengthy although I think the content is at least original and interesting for a researcher in my field. So my guess is that he doesn't have time to go over it and does not care enough to meet me for a discussion. There is a possibility that he might  have missed the email. There is another complication that he suggested one time if I wanted him to supervise my research but I have already chosen another professor as my supervisor at that point. So he could have felt uninterested after knowing that, although we had one more discussion after that incident. 

Question:
How and when should I follow up with another email? I really want  his reference but do not want to appear like a burden (that's why I did not reach out to him for the whole summer until now). I may be able to go to his office uninvited but I'm not sure that'd be a good strategy. 

Thank you!
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.