From Wikipedia: "Regarding the monopoly on delivery of letters, the report notes that the monopoly is not complete, as there is an exception for letters where either the amount paid for private carriage of the letter equals at least six times the current rate for the first ounce of a single-piece First-Class Mail letter (also known as the "base rate" or "base tariff") or the letter weighs at least 12.5 ounces."
https://en.wikipedia.org/wiki/United_States_Postal_Service#2...
edit: Here is the law https://www.law.cornell.edu/uscode/text/39/601