The official rules, as posted on the USPS website, do allow for stuffed envelopes. Details have been posted here on the forum quite a number of times.
No more than 4 pounds per envelope, though!
Seriously... you could not fit 4 pounds of documents in an envelope that size. Nor could you fit 4 pounds of fabric. Three, maybe...
I have always been able to send stuffed envelopes. The only problems I have encountered were on the receiving end. I have had to call the destination Post Offices and speak to the postmaster and cite the rules, regulations, and applicable rulings to them. I have also on occasion had to have my local USPS Business Services Specialist call the destination Post Offices on my behalf.
I think this was more of a problem in December-January when the rules were in flux and updated memos regarding USPS rulings had not been sent to (or read) by all the branches. I have not had any problems since February.