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?