How Does a Black Hole's Size Scale with Mass?

Why can a more massive black hole have a larger horizon without being a denser ball?

You defined rₛ, M, M☉, G, and c; used a linear mass-radius relationship across four scales; and kept horizon size separate from a solid surface or measured interior density.

Three black-hole horizon silhouettes increasing in size across a star field, each edged by a thin amber lensing glow. — Vastward artistic reconstruction. The three silhouettes communicate that horizon scale grows with mass. They are not direct images and are not drawn to one shared linear scale.

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