Your assumptions aren't quite correct.
The gravity at the surface depends on the mass of the planet AND the radius. A larger radius and lower density planet can still have a 1g surface gravity.
But when you increase the radius, you also increase the distance that it takes to get down to a given lower value of g.
E.g. For earth with a radius of 6000 km (rounding here) for 1g, you have to move to 12000 km from the centre to get down to 1/4 g.
For a lower density planet (less iron in the core...) suppose that the radius was 7500 km. For this planet you would have to be 15,000 km from the centre to get to 1/4 g.
If you give a planet 2 times the mass of earth, but 1.414 times its radius you still get a surface gravitation of 9.8 m/sec. But escape velocity has increased from 11 and change km/s to 13 and change. This drastically increases the energy needed by a gas molecule at the top of the atmosphere to escape. So the planet doesn't lose gas nearly as fast.
This planet will have a thicker atmosphere all other conditions being equal. How much thicker? Probably lots. Venus isn't much different from earth in either mass or diameter but it has a lot more atmosphere. On Earth most of the CO2 is in the form of carbonate rocks. Earth has a moon that creates tides in the atmosphere. When the tide is high, it's easier for gas molecules to escape. Larry Niven in one of his stories/articles wonders if a big moon is an essential ingredient to clearing enough of the atmosphere for sunlight to reach the surface. Alas we don't have enough examples.
I am skeptical about getting a thick enough atmosphere to swim in with your present scenario. But normal pressures and lighter gravity could do the trick. See Heinlein's "Menace from Earth" which features flying in the air storage caverns of Luna City.
M = 1.25 M_earth
R = 3 M_earth gives you an escape velocity of 7 km/second, and a surface gravity similar to that of the moon. This much of a radius increase means 27 times the volume, but only 1.25 times the mass, so the overall planet has a density about 1/5 that of earth. Not a lot denser than water.
Play around with the calculator. I suspect that even a 1/3g human powered flight isn't unreasonable, especially if you run at an air pressure of 3 atm or so.
It is NOT clear to me what a 3 atm surface pressure does to weather.