When I was a child I wondered why Superman didn't have to wear a spacesuit on Earth, since one explanation for his super strength was the much lesser gravity on Earth and humans would have to wear spacesuits to survive on the Moon despite the gravity difference not being enough to make them as strong as Superman.
And I was quite skeptical about science fiction stories where the Moon had a breathable atmosphere.
When I was 12 I read "He Who Shrank" (Amazing Stories, August 1936) by Henry Hasse" and was doubtful about the subplot involving a species who migrated from their home planet to its moon. I was very skeptical about both the planet and the moon being naturally habitable for a single species. "He Who Shrank"is otherwise a memorable story — I had a dream with a variation of its plot recently.
In the Next Generation episode "The Host" 13 May 1991:
LEKA: The people on our moons have been in discord ever since they migrated from our planet five centuries ago. To us on the planet They're like two squabbling children. We try to help settle their arguments by not taking sides, but this time we are at a loss.
So fifty five years later writers were still not worried about smart children laughing at them for suggesting that a species that originated on a planet could survive on naturally habitable moons of that planet. See also the habitable for Bajorans moons of Bajor in Deep Space Nine.
Of course by then the idea of terraforming planets and moons to make them habitable was well known. See Project Genesis in Wrath of Khan and "Home Soil". So maybe the writers of "The Host" assumed that the people of Peliar Zel had to terraform their moons before settling them.
Thus I suggest that you might face a problem in nomenclature. Calling the larger body a planet and the smaller body a moon may make some readers think that it should be impossible for both worlds to be naturally habitable for the natives of the larger world — or for humans if humans are involved in the story.
One alternative is to describe the two worlds as a double planet instead of a planet and a moon. But not twin planets, of course.
The Earth and the Moon have sometimes been described as a double planet, and after Charon was discovered Pluto and Charon were often described as a double planet instead of a planet and its moon. So you might do well to have some of your characters discuss or argue whether the smaller world is a moon or the smaller part of a double planet.
And maybe include some ironic counterpart to the way that in our solar system the first asteroids to be discovered, and later Pluto, were considered planets and then demoted in status.
Another method would be to have the explorers from the planet talk about how their people have dreamed and argued and studied about the possibility of life on their moon and the probability that it might be habitable for them. Point out that for the people of that world a dream that died over a century ago for Earth people is a reality and how wonderful that is for them. Make it in part a wish fulfillment story for us Earthlings.
A third method — and I think you should use all three — is to show your work. Or, considering your question, the work of whoever you get to do the calculations for you.
Have calculations done to show that the smallest sized and the largest sized habitable worlds can differ in size enough to be described as a planet and its moon, or alternately as sister worlds (but not twin worlds) in a double planet.
I found a discussion of the habitability of exomoons, natural satellites of extra solar planets:
A minimum mass of an exomoon is required to drive a magnetic shield on a billion-year timescale (Ms≳0.1M⊕; Tachinami et al., 2011); to sustain a substantial, long-lived atmosphere (Ms≳0.12M⊕; Williams et al., 1997; Kaltenegger, 2000); and to drive tectonic activity (Ms≳0.23M⊕; Williams et al., 1997), which is necessary to maintain plate tectonics and to support the carbon-silicate cycle. Weak internal dynamos have been detected in Mercury and Ganymede (Gurnett et al., 1996; Kivelson et al., 1996), suggesting that satellite masses>0.25M⊕ will be adequate for considerations of exomoon habitability. This lower limit, however, is not a fixed number. Further sources of energy—such as radiogenic and tidal heating, and the effect of a moon's composition and structure—can alter the limit in either direction. An upper mass limit is given by the fact that increasing mass leads to high pressures in the planet's interior, which will increase the mantle viscosity and depress heat transfer throughout the mantle as well as in the core. Above a critical mass, the dynamo is strongly suppressed and becomes too weak to generate a magnetic field or sustain plate tectonics. This maximum mass can be placed around 2M⊕ (Gaidos et al., 2010; Noack and Breuer, 2011; Stamenković et al., 2011). Summing up these conditions, we expect approximately Earth-mass moons to be habitable, and these objects could be detectable with the newly started Hunt for Exomoons with Kepler (HEK) project (Kipping et al., 2012).
This indicates a minimum mass for the smaller world of at least 0.25 Earth masses and a maximum mass for the larger world of no more than 2.0 Earth masses, thus indicating the difference in mass can be almost 8 times the mass of the smaller world.
Since the sister planets — or planet and moon — would almost certainly be tidally locked both will rotate with the same period as their obit around their center of mass. The days of both will be equal to their month.
But the faster a world spins the more likely it is to generate a strong magnetic field that protects the outer atmosphere from charged particles. So the orbits of the two worlds need to be designed to give them short enough months and thus fast enough spin.
Some studies suggest that even extremely slow rotation would allow for substantial magnetic shielding, provided convection in the planet's or moon's mantle is strong enough (Olson and Christensen, 2006). In this case, tidal locking would not be an issue for magnetic shielding.
(from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3549631/)
If correct that may greatly lessen the necessity to make the orbits as short as possible.
Note that the article discusses the habitability of exomoons orbiting gas giant exoplanets in the habitable zones of their stars (orbiting "Hot Jupiters") instead of exomoons orbiting Earthlike planets, which may modify some of the calculations a bit.
you will need to calculate both the surface gravity and the escape velocity of both the worlds. It is a well known fact that long term exposure to the microgravity or weightlessness of Earth orbit causes health problems for human astronauts. It is not known if long term exposure to the lower gravity of Mars, for example, would have the same effect on human health.
Thus you can choose to:
Ignore health effects of lower gravity on your natives of the planet.
Have their scientists use centrifuges set to simulate the gravity of their moon in their orbiting space station and discover that the natives of the planet don't suffer any bad effects from long term exposure to it.
Have the characters from the planet make only short stays on their moon.
Have the space ship include centrifuges to simulate the gravity of their planet.
Have the characters take other precautions against the long term effects of lower gravity, much as Earth astronauts do during long stays on space stations.
Have the characters discover the problem during a long stay on their moon, and find out they need to return home immediately, preferably when for other reasons it is least possible or desirable.
Have the planet and the moon have very similar surface gravity despite the differences in their sizes and masses, so that it isn't very surprising that the natives of the planet are not harmed by the minor difference in surface gravity.
Or some combination of two or more of the above.
If you make two very dissimilar worlds have similar surfaces gravity despite having very different masses and diameters, they will have to have different densities, despite there being both upper and lower limits of density for Earthlike worlds. The smaller world will have to be denser and the larger world will have to be less dense.
Both the worlds will have to have high enough escape velocities to retain their atmospheres for geological time spans. The escape velocity of the larger world should be as low as is possible, since Earth's is certainly high enough to make reaching orbit and leaving orbit very difficult. Making the larger world less dense (within practical limits) will keep its escape velocity as low as possible.
