In opera, vocal weight is a term used to describe how "light" or how "heavy" that a voice is and by extension what kind of roles that it is suited to.
Lighter voices are associated with lyric voices while heavier voices are associated with dramatic voices; lyric voices are usually brighter, sweeter, and more agile while dramatic voices are usually powerful, rich, and darker than their lyric counterparts.
Spinto voices, usually limited to tenors and sopranos, are a kind of bridge between lyric and dramatic voices, "light heavyweights" in a manner of speaking.
Vocal weight may or may not be obvious immediately; a singer needs a number of opinions before any determination is reached. Vocal weight is also a strong mark of who gets to sing what in opera. Lyric voices usually play more vulnerable characters while dramatic voices usually play bold, strong characters.
Lyric voices are strong, but they're light; they don't like to sing very loudly very often and often sound forced when they do so. Lyric voices are designed for smooth, sweet singing, agile passages and clear diction.
Dramatic voices are bigger and heavier than lyric voices and their power makes them more difficult to maneuver through flowery coloratura passages, but dramatic voices are designed to sing loudly; they can sing over a large orchestra more easily than lyric voices can and are filled with emotion in addition to power.
Spinto voices are light but powerful and are essentially lyric voices with a strong dramatic edge (squillo, or "ping"), which allows them to cut through a full orchestra (rather than sing over it like a true dramatic voice).