This isn't about physical weight but how heavy something looks. Larger, darker, rougher-textured and more angular pieces all read as visually heavier. Cluster the big dark furniture on one side of a room and it feels lopsided regardless of what actually weighs more.
There are two ways to balance it: symmetrical balance, mirroring the same thing on both sides, and asymmetrical balance, where different-sized things are placed to carry equal visual weight. A large dark bookshelf on one side, for instance, can be offset on the other by a smaller but brighter lamp plus a couple of plants — count and brightness making up for size.
After arranging furniture, converting a photo of the room to grayscale is a quick way to check: with color's illusions removed, pure size and contrast make it obvious whether the weight has drifted to one side.
When to use
Check this when a room feels lopsided even after everything is placed. Convert a photo to grayscale — if one side still reads heavier, thin out that side or add something bright to the other.