Now you need to define 'bigger' in this context...
It's a range of factors, but the primary one is mass.
Escape velocity applies to gases as well - e.g. Helium escapes from the Earth's atmosphere.
The lower the mass, the more gases escape.
Solar wind is a factor - the high energy particles strip molecules from the atmosphere, so proximity to the star, its type and current lifecycle stage all combine in how that affects a planet.
Then you've got the magnetic field which can deflect those particles and protect the atmosphere - that's one reason the Earth is habitable and Mars is not.
Mars is smaller, so its core cooled faster and it isn't generating a magnetic field anymore.
Nice summary of the various factors here - https://en.wikipedia.org/wiki/Atmospheric_escape