It sounds like you're somehow associating oxygen with gravity. The two have nothing to do with each other, except that if you get enough oxygen in one place (say, several trillion tons), you will be able to feel its gravity.
No, things do not "float" on other planets. They may fall more slowly, or more rapidly, than they do on Earth, depending on the surface gravity.
Visit the Apollo Lunar Surface Journal and look at the pictures and films that were made on the Moon. The Moon has no atmosphere at all, practically speaking, and things do not "float around" there.
"For shame, gentlemen, pack your evidence a little better against another time."
-- John Dryden, "The Vindication of The Duke of Guise" 1684