Word Origin & History
Plimsoll"mark on the hull of a British ship showing how deeply she may be loaded," 1881, from Samuel Plimsoll (1824-98), M.P. for Derby and advocate of shipping reform (which were embodied in the Merchant Shipping Act of 1876). Sense extended 1907 to "rubber-soled canvas shoe" (equivalent of Amer.Eng. sneakers)
because the band around the shoes that holds the two parts together reminded people of a ship's Plimsoll line; sense perhaps reinforced by sound assoc. with sole.