MY understanding of Hawking radiation is mostly classical-
There are particles that when they interact with matter, the mass of both particle and antiparticle vanishes. Generally, they form in pairs from energy and cancel out, creating energy back.
99.9999 repeating % of the time, a particle pair near an event horizon either both falls in, or both escapes. we can safely ignore them.
If the antiparticle falls in the blackhole, it makes the black hole some infintismly small fraction lighter, improving the odds that the antiparticle's partner can escape. That partner is Hawking Radiation.
If the partner falls in, however, the blackhole is some infintismly small fraction heavier, reducing the odds that the antiparticle can escape.
This means that, 1)more mass will "escape" from a black hole than will be added to a black hole, like this, and 2) the lower the mass of a black hole, the greater the odds of a single antiparticle affecting the escape of it's partner, and the more Hawking radiation is generated.