I think, the most prevalent earth disease that can be cured by a 2G gravity, is called "human life".
We do not have any data on sustained high-g environments, but there are several extrapolations that can be made from current earth issues dealing with / caused by gravity.
In higher gravity, breaking bones becomes a lot easier since everything exerts more force. It is not recommended for someone with Brittle Bone Disease to experience such an environment as their bones already break easily when in normal gravity. And I expect that stress fractures will become more common.
On the other hand, Osteoporosis might be slowed down by this. Current pervention / treatment mechanisms already consist of working out to put the bones under pressure so that more bone mass is built / current bone mass is not lost due to age. Higher gravity would help quite a lot with this.
However, 2G will definitely be Not Good for joints. Knee joints especially, since they will have to carry twice the load. The cartilage inside will get worn down even quicker, so you won't have 60-year-olds getting new knee joints regularly, but maybe already 30-40 year-olds.
Back problems should also become a lot more prevalent than is already the case nowadays.
Since the disks get compressed by twice the weight, they will wear down more quickly, and slip easier. All common current malformation (hunchback, hollow-back, misaligned spine) will cause very severe issues right from the beginning, with things escalating to slipped disks very quickly.
If you want to have any chance at preventing back problems in 15-year-olds already, you will need a very heavy exercise regimen targeting the back muscles specifically.
This is the primary reason why 2G will probably cure the disease of "human life". Our heart and veins are not built to sustain a pressure necessary to fight 2G until the blood goes up to the brain. Even with compression suits preventing the blood from pooling in the feet (that the colonists would have to wear 24/7 -- and do you have any idea how annoying it is trying to get into compression socks even nowadays, those against varicose veins?) the blood pressure itself will have to rise to give the brain all the oxygen it needs when standing upright.
And high blood pressure comes with its own problems, all of which are already known nowadays.
Sleeping will also become quite a bit less restorative, especially if you are sleeping on your back. Gravity will compress your chest more, and you will probably need a muscle tonus close to being awake just so that you can breathe. Snoring should also become more common in such positions... and Sudden Infant Death too (caused by small babies lying on their stomach and just stopping breathing)
Bed sores (and sores in general) will become more common. They are caused by the body's weight pressing down so hard that some of the skin at the bottom (where the most pressure is) doesn't have circulation flowing for long enough to have cells die off.
Probably the second factor contributing to the disease cure.
This is what I know the least about, but potentially one of the most insurmountable fatal cause.
I don't think that at 2G there is enough atmospheric pressure for the issue of different absorbtion of oxygen / nitrogen mixes to occur (look at breathing mixes for divers having to dive very low). As far as I know, most of the Brooklyn Bridge Worker issues came from breathing sea-level atmospheric pressure air while working under at least 2 atmospheres of pressure. This you can prevent by giving your colonists the appropriately pressured air.
However, the absorbtion rate of membranes of all kinds will be changed. Maybe not by a lot, maybe by just enough to make sustained life in 2G impossible.
Where are membranes in the body?
- lungs: absorb oxygen, release carbon dioxide
- cells: absorb oxygen and glucose from blood, remove cellular waste products
- nerves: nerve impulses jump from one nerve cell to another by one cell releasing calcium / potassium / ... ions into the gap between nerve cells. Those ions need to diffuse across the synaptic gap to be absorbed by the next nerve cell in the line
- intestines: absorb glucose, fats, etc. from digested food
- kidneys: remove waste products from blood
Of course, none of those systems will be destroyed completely by 2G (otherwise, humans would not enjoy rollercosters that much or survive fighter planes or being shot into space). But it would be enough to have them functioning at only 95% efficiency to make life suddenly a lot harder when trying it long-term.
To be able to live somewhat practically in 2G gravity, every single person requires a fitness-level quite a lot higher than what we have today.
Overweight will become pretty much a non-issue - for one, just moving around and doing nothing will already be quite exhausting. For another, every single pound of weight on you will make life harder. And you will constantly have to keep your muscles in shape if you do not want to have severe back problems 2 years down the line.
If you want to be active in a 2G environment, you can compare the requirements most closely to soldiers carrying a heavy backpack on long marches. But even they can just take off the pack and rest for a couple of minutes, not to mention that they do not sleep with it lying on their chests...
Moving Colonists from Earth to Planet High-g
If you nevertheless want to send your colonists to this planet, you should do one of the following:
- have the space ship slowly increase its acceleration from Earth-G to High-G during the course of the voyage so that the colonists can give their bodies weeks or months to gradually get used to higher gravity. (since braking also counts as acceleration, negative acceleration, you can keep up the higher gravity until just minutes before landing). Just dropping them on the planet from 0G in space and then hoping everything will be fine and dandy -- doesn't work
- build a rotating space station in orbit above the planet that can simulate all gravities you need, from High-G at the end of the arm, to Earth-G somewhere in the middle of the arm, to weightlessness in the center. Gives your colonists time to recover from the 2G strain, or to train to take it in the first place
Even so, I am pretty sure that such a high-G environment will heavily stunt children's growth, and raise infant mortality incredibly high (due to the adverse conditions).