First we must compare the surface gravities of Earth and Mars. Planet Earth has 2.63 x more gravity than Mars.
So a Martian going to Earth is similar to an Earthling visiting Jupiter a bit closer to its poles. Humans live in the Earth's gravity for (almost) their entire lives and I think they couldn't spend days on floating cities on Jupiter since Jupiter's 2.5-2.7 g would prevent them standing up. Something similar counts for people born on Mars. If they tried to visit Earth they wouldn't be able to stand up. They'd have weaker muscles and bones.
As with astronauts who visit Mars for two years (the length a manned stay on Mars is expected) I think they will eventually adapt back to Earth's gravity. Two astronauts already spent more than a year on the ISS (in weightlessness). On a Mars mission you spend 6 months in weightlessness, 2 years in 0.38 g and another 6 months in weightlessness, so I think returning from a journey to Mars is manageable for the human body. Of course, the more time you spend on Mars, the harder the body has to readapt to 1 g (or 2.63 g from a perspective from Mars). But if these astronauts weren't born on Mars they would eventually re-adapt. It may take months if not years, but I'm sure they would.