First, we must realize that we cannot predict what each individual person will do. All we can do is to predict what will happen on average. On average, the laws of economics tell us that people will tend to take better care of themselves if they have to pay for all of their medical expenses. However, it is not clear how much better people would take care of themselves.
The laws of economics tell us that people will, all other things being equal, try to avoid behaviors that will cost them money. The more the price of the behavior increases, the more they will try to avoid it. If overeating and failing to exercise were to lead to greater out of pocket costs, people would generally do more to avoid those things.
The problem is that they might not try very hard to avoid them. The reason for this is that there is not a clear, inevitable, and proximate cost to those behaviors. If I overeat and do not exercise, I am certain to gain the benefits (the pleasure of eating and relaxing). It is possible that I will end up incurring medical costs, but that might not happen and, if it does, it will probably be far in the future.
For this reason, the changes in people’s behaviors might be very limited. People might not forego pleasure in the present in order to avoid the possibility of incurring costs at some vague point in the future.