If you take two planets of the same density, but one with a radius that's twice as large, the mass and volume is going to be 8 times higher (2³), while the radius is only going to be twice as high.

The gravitational field is inversely proportional to the distance squared...

But escape velocity is only inversely proportional to the distance... This means that if you made a really dense, small planet where the surface gravity is identical to earth, it would still have a much lower escape velocity, so the gases are going to be likely to escape due to atmospheric escape; when a molecule is moving at a higher velocity than the escape velocity of the planet.

Thus, a smaller planet with the same surface gravity would lose it's atmosphere due to atmospheric escape at a much higher rate than a larger planet.

You can take it the other way, and have a hypothetical megaplanet that has a lower density, but because of it's enormous size, it still has an earth-like surface gravity, but it's escape velocity could be so high that a hypothetical civilisation could be stuck there and might never be able to escape their planet's gravitational binding energy, thus never becoming an interstellar civilization. In theory, a large enough black hole could have an event horizon where the acceleration is the same as on our planet's surface, but the escape velocity would literally be the speed of light and people would never be able to leave.