Looking into the origin of ply as a result of thinking about the expressions “plying [someone] with drinks” or “plying [someone] for information,” I found etymological connections to an interesting variety of terms. Here are some words related to ply based on its Latin ancestor.
Ply derives from the term plicare, meaning “to fold.” Generally, words ending in -ply that have a long-i sound are related to ply and each other; those with a long-e sound (such as deeply) merely have a root word ending with p, followed by the adverbial ending -ly. The exceptions to the first class are comply and supply; in each case, the second syllable stems from plere, the Latin word meaning “to fill” (though the sense of “agree” for the former is influenced by ply).
The senses of ply in the first sentence, and others, are from a shortening of apply and derive from the related meaning of “bend”; when you ply someone with drinks or for information, you are bending (that is, manipulating) that person. Another meaning of ply is “travel regularly,” related to the sense in the phrase “ply a course.” One can also ply one’s trade, meaning “conduct business” or suggesting diligent practice or performance. The name for the ballet movement called the plie, from French, is related.
Ply is also a noun meaning “a layer” or “a fold”; plywood (and its daffy derivate, plyboo, referring to plywood made from bamboo) stems from this word, and it is the source of references to strands of yarn or layers of fabric or paper. When you multiply, you create many folds; multiply originally meant simply “increase” and only later acquired its mathematical sense of increasing an amount by an equal amount a given number of times. Similarly, to duplicate or triplicate and so on is to create two or more folds or iterations.
A plier, meanwhile, is someone who or something that bends or folds, hence pliers for the name of a hand tool. Something that is easily plied is pliable or pliant; the former generally refers to an object, while the latter adjectival form is usually applied to a person who is submissive or easily influenced. (The synonym compliant is based on the unrelated comply.)
Reply, meaning “to give an answer,” originally carried over into English the literal Latin meaning of “fold back,” but that sense is obsolete. Meanwhile, apply basically means “to bring something in contact with another” (and an application is something that accomplishes this task) and to imply is to involve or enfold, while to implicate someone is to involve or enfold them, and an implication is something that does just that.
Employ, interestingly, comes from the same root word as imply, but it acquired a primary meaning related to hiring. Implicit, referring to something implied, is also related to imply. Something made explicit, by contrast, is unfolded, or revealed, and to explicate is to unfold, or explain, something, an action called an explication.
To complicate is to make something intricate as if it has been folded; a complication ensues. Complicit and its noun form complicity are related, as is accomplice, denoting someone who has been enfolded in a crime or a scheme. Complex, meanwhile, is also related, stemming from the Latin word for “braid” or “weave,” as is the rare antonym simplex and their noun forms complexity and simplicity.
Plait and its variant pleat, each of which serves both as a noun and a verb, share an origin with ply through French, as does plight, which originally had a neutral connotation of “condition” but later developed a sense of being in danger. (An unrelated meaning of plight, which stems from pledge, was “promise”; the negative sense of plight that means “a dangerous situation” may derive from confusion with the other meaning of plight, in that a pledge or promise often entails risk.)