Should I use affiliation?
This is more in the realm of opinion than fact, but I would always use the affiliation. This gives the reader a bit of context that will most likely increase your credibility. If the reader is open to believing what you say even before beginning reading the paper the mindset will be different than if it is just a bit of work by a random, completely unknown person. 

Of course, once you become Stephen Hawking the affiliation is no longer needed. 

But for the rest of us, knowing that we did the work as a faculty or staff member at the University of the Universe (or whatever) will give us that opening that allows a fairer reading of the work.