Visual weight is the perceptual heaviness of an element in a frame. It depends on size, brightness, colour saturation, and isolation. A small bright thing on a dark field can outweigh a large muted shape; a single figure with empty space around it carries more weight than the same figure surrounded by clutter.
Why it matters
Compositions feel balanced when visual weights work together rather than crowd or cancel each other. The rule of thirds is one heuristic for distributing weight across a frame, but it is the symptom rather than the cause.
Spend a week looking at images you already like and pointing at the heaviest area. After a few hundred frames, you will start composing for weight without thinking about it.