Last night I re-watched one of the BBC programs from their series Wonders of the Solar System. This just happened to be the one about atmosphere.
We need the atmosphere to exist, it controls so many of the planet's systems. If there is too little e.g. Mercury, then there is nothing to slow down objects and the planet gets heavily bombarded, also it gets the full effect of the harmful rays from the sun. With the lack of atmosphere the change of temperature between night and day is very high. Mercury basically lost it's atmosphere very quickly because of it's low gravity and high heat.
Jupiter is the opposite, it has a very deep atmosphere, with no solid centre. The result is massive storms, the red spot is one that has been raging for at least 300 years. It holds on to it's atmosphere because of it's surface gravity which has been calculated as being 2.53 times that of the earth (Jupiter does not have a solid surface so I presume that this gravity is at it's liquid surface). It is also colder than the earth, -108.15 C compared to the earth's 15 C. The density is less than 25% of that on the earth, it's mean circumference is 11 times that of the earth.
So whether or not a planet (or moon) can support life as we know it is dependent on many parameters, which include it's gravity.