Visual weight is what designers mean when they say a room "feels balanced" or "feels off". It's not about literal weight — a small dark sculpture and a large pale armchair can have similar visual weight. The factors that increase visual weight: size, dark/saturated color, dense texture, high contrast against the surroundings, sharp edges.
Good compositions distribute visual weight evenly across the eye's field. A heavy piece in one corner needs counterbalance — another heavy piece in the opposite corner, or several lighter pieces summing to similar weight. Symmetry handles this automatically (matching pairs). Asymmetric arrangements have to balance manually.
This is the principle behind why a minimalist room with one bold black painting on an otherwise plain wall feels great, while the same room with two competing paintings feels chaotic. The single painting balances the rest of the room's emptiness; two paintings create a tension neither resolves.