I’ve posted before about mailing folded self-mailers. In addition to the size and weight requirements for standard mail there is also a limitation on stiffness: the item has to be flexible enough to feed through the machines that process mail, so you could not for instance mail a rigid piece of flat plastic (without paying a special handling surcharge) even if it met all the other guidelines.
So here’s a weird question that I haven’t found an answer to: what’s the flimsiest a piece of mail can be? If for example you wanted to an a-hole and contrive a letter and envelope out of the most gossamer paper you could. What would the USPS reject, and what would be the dividing line?
I’m not sure there would be a rejection.
Perhaps, instead, the addressee would receive a plastic bag containing the salvaged shreds of the article and a note indicating the article had been damaged by processing.
USPS mail standards says minimum thickness is .007 inch. Anything thinner is subject to a non-machinable surcharge.
Okay, although I wasn’t planning to put this to the test, I don’t have any thousandth-inch calipers. I’m now curious to look up the thickness of standard grades of paper. ETA: standard letter/printer/copier paper is about .004, so two thicknesses of that would be fine.
never mind 
have you measured a classic old school air mail onionskin paper? do they still make it?
Sources online claim it was about 46 microns, or 0.0018 inches. So an envelope containing one folded sheet would total 0.0072 inches, about the limit.
I have [somewhere] a few old letters stuffed in the back of my grandfathers desk and the paper is named well - it has that funky thin crinkly onionskin texture. I actually sort of like the texture =)