It has been observed that people with a low BMI (body mass index < 25) are generally healthier those who have a high BMI, that is classified as overweight or obese. However new and intriguing findings by researchers at the University of Helsinki, Helsinki and Copenhagen University Hospitals, Danish Epidemiology Science Center and National Public Health Institute in Finland have shown that those overweight individuals who wish to loose weight and succeed have a higher mortality than those who do not loose weight.

Similarly those who had a low BMI and gained weight also had an increased mortality.

It seems that the thing that damages health the most is fluctuations in weight rather than the actual weight of a person.

Critics of studies of this nature in the past have pointed to weight-loss associated with illness, in particular cancer, as confounding the results however the Helsinki study removed those subjects with illness from the study.

They say

In people who have medical conditions related to obesity, losing weight is obviously desirable, emphasize the researchers. But overall, preventing people, especially children, from becoming overweight in the first place seems crucial, since this work suggests that once weight is gained losing it again may not be good for health.

Read a little bit more here.
Or a lot more here (if you speak Finnish)