OK, try it in the opposite direction: having constructed a doubletalk-drive spaceship and travelled to another star’s solar system, we encounter a planet much like Earth but with a heavier gravity. What are the consequences? At what point is atmospheric pressure a problem? Does increased gravity (say a steady 1.4, or 1.6, or 2.0 G) come into play as causing problems before that?
Well, yeah. No jumping! You all are missing the point of the fun stuff: 
what if we could lower Earth’s gravity a little bit. How much before we could do some massive jumping? (Get it? …gravity…massive…hehe).
I doubt increases in air pressure due to gravity alone would be an issue at any viable gravity level. If we assume that pressure increases linearly with gravity, then even a 2g field would have an air pressure of ~30psia/2bar, and long submersion divers handle that kind of pressure indefinitely. At higher pressures oxygen toxicity due to increased partial pressure of oxygen can become an issue, but assuming our linear scale the level of gravity to cause that would be literally crushing. (In truth, higher gravity would have dramatic differences on planetary development and atmospheric composition, but we’ll ignore that for now.)
Higher gravity, on the other hand, is going to be a significant issue. Even a small increase in gravity–say, 1.2g–will increase the load on joints and tissue. A healthy, fit adult could probably tolerate this for an extended period without dramatic issues as long as he did not overexert himself (no marathons, and be careful with the squats), but I suspect it would cause developmental problems in children and exacerbate chronic health issues (like arthritis or high blood pressure) in older adults.
Sustained gravity levels beyond 1.5g would probably cause significant health issues in even fit adults. It’s not just the extra weight that they would be carrying around–which is managable–but the effects on the circulatory system and specifically the heart, which is designed to pump blood in a 1g field. I would guess that there would be other issues as well, including muscle tissue–under constant, unrelenting demand to be stronger than they were evolved to do–leeching vital nutrients from the rest of the body. The calcium metabolism is a particular issue, since the competition between needs for skeletal construction and the demand to regulate cellular processes pertaining to respiration (calcium acts as a regulator in the Krebs cycle). You could increase calcium levels via dietary supplements or, if necessary, by direct injection, but there are other health implications to that.
In general, living in higher gravity levels is a lot more complicated than just the extra weight you’d have to carry. This would probably make a good question for a Staff Report to obtain a more comprehensive answer.
Stranger
Ok, but I’m asking about less gravity and it’s health effects or enviro effects. : )
Atmospheric pressure need not be a problem. A planet’s gravity puts an upper limit on how much mass it can hold, but really, there’s no lower limit. Which is a very good thing for us, because our own Earth is way below the upper limit. With our mass and distance from the Sun, there’s no reason we couldn’t have an atmosphere hundreds of times thicker than the one we have. We just don’t happen to have enough air for that.
So we could have (theoretically) had the same atmosphere and much less gravity,too? (Or is that “have had had,” or just “have”?)
Yeah, I was thinking of Venus. Smaller than earth, but what an atmosphere. Also there’s Saturn’s moon Titan , with an atmosphere 10 times deeper than Earth’s and with a surface pressure 60% greater, but with only something like 1/10th the gravity.