Shakespeare's sonnets were published in 1609, no doubt without authorization, by the unsavory Thomas Thorpe (1580-1614), described as "a publishing understrapper of piratical habits" who "hung about scriveners' shops" in order to pinch manuscripts.
A friend sent me the above, and knowing I like words, he asked me about "understrapper." Looking it up, I see that it means a "petty fellow," but I've not heard it before. Have you? Does its etymology have anything to do with putting together the words "under" and "strapper," do you think?
Just wild speculation on my part, but since the lowest part of a saddle is the girth strap, it might allude to that. He wouldn't be fit to sit atop the horse.
I can date it to 1704 but have found no reference to its roots. It seems reasonable to assume that it was to do with horses as that was certainly a lowly job at the time.
The OED Online gives as one of the meanings of strapper (1828) was "One who straps or grooms horses, chiefly Austral. in later use," and that, by 1854, strap became a transitive verb meaning "To groom (a horse)." It seems likely to me that these meanings were derived from understrapper, "An underling; a subordinate agent; an assistant." (1704, as Doad said).