Why does the word light as in weight mean illuminate?

Run, square, right, can, wash, clear, amd the list goes on. Light can mean not heavy or light by which we see. The following text is a cut and past job from the Yahoo! Dictionary: "light 1 (lt) KEY NOUN: Physics Electromagnetic radiation that has a wavelength in the range from about 4,000 (violet) to about 7,700 (red) angstroms and may be perceived by the normal unaided human eye. Electromagnetic radiation of any wavelength. The sensation of perceiving light; brightness: a sudden light that made me blink. A source of light, especially a lamp, a lantern, or an electric lighting fixture: Turn out the lights when you leave. The illumination derived from a source of light: by the light of the moon. The particular quantity or quality of such illumination: moved the lamp closer to get better light. The pathway or route of such illumination to a person: You're standing in his light. A mechanical device that uses illumination as a signal or warning, especially a beacon or traffic signal. Daylight. Dawn; daybreak. Something, such as a window, that admits illumination. Architecture One of two or more openings in a window divided by a mullion or mullions. A source of fire, such as a match or cigarette lighter. Spiritual awareness; illumination. Something that provides information or clarification: threw some light on the question. A state of awareness or understanding, especially as derived from a particular source: in the light of experience. Public attention; general knowledge: brought the scandal to light. A way of looking at or considering a matter; an aspect: saw the situation in a different light. Archaic Eyesight. lights One's individual opinions, choices, or standards: acted according to their own lights. A person who inspires or is adored by another: My daughter is the light of my life. A prominent or distinguished person; a luminary: one of the leading lights of the theater. An expression of the eyes: a strange light in her eyes. Light In Quaker doctrine, the guiding spirit or divine presence in each person. The representation of light in art. VERB: light