"Sleight of hand" is one tricky phrase. "Sleight" is often miswritten as "slight" and for good reason.
Not only does the expression convey an image of light, nimble fingers, which fits well with the smallness implied by "slight," but an alternate expression for the concept is "legerdemain," from the French léger de main," literally, "light of hand."
"Sleight" comes from a different source, a Middle English word meaning "cunning" or "trickery." It's a wily little word that lives up to its name.
Source: 12 Old Words That Survived by Getting Fossilized in Idioms, from Mental Floss