As far as my understanding of gaseous & planetary physics goes (which isn't very far), while there are a number of things that can cause a thin, very thin, or less atmosphere to form, or a normally-dense atmosphere to be partially removed, from a 1-G world, isn't the only way to get a more dense atmpsphere by having a gravity of more than 1?
I have no idea how it would form, but replacing the "inert" nitrogen in earth's atmosphere with a heavier inert gas would make the atmosphere denser without needing a higher gravity. Venus has less gravity than earth but a denser atmosphere. Same concept, different gas mixture.