Being moderately overweight is not protective in overall mortality.

One of the problems in research is when you oversimplify or unintentionally skew your data.  When you do this sort of examination of data, you miss the proverbial forest because you are looking at all the trees.  You need to look at the right data and not too much nor too little.  In other words, you have to have the proper inclusion and exclusion data.  

A few years ago, a study looked at being overweight and whether it was protective against overall mortality.  The study in question was from 2013 and was published in the Journal of the American Medical Association​[1]​.  It was a meta-analysis that looked at 97 prior studies to determine the relationship between body weight and all-cause morbidity and mortality.  The researchers were surprised by their data and determined that moderate obesity with a BMI of 25-30 was protective against all-cause mortality.  The findings were counter to what was expected, and the publication of the results produced an avalanche of articles that touted the protection that obesity reportedly provides.  

Since the publication, a growing number of experts have questioned the results and claimed that the results were suspect due to poor measurements of data.  For example, who do we not know that the obese do not lose weight when they become ill and move into a normal weight range and increase the mortality of the normal weight range.

A new study from 2017, looked at three studies with 225,000 subjects[2].  Instead of looking at current weight, this study looked at both current weight and the maximum weight of 16 years.  This study revealed that obesity was not protective against mortality.  

The bottom line: BMIs at the extremes (low and high) are a risk if you become ill and may predispose you to certain illnesses.  A single BMI is not useful for determining risk.  I hazard you to think that weight loss is not good for you based on the early study.  Weight loss, in general, is better for the health of an obese subject so I would recommend it unless they have a condition that would do better with a higher weight such as cancer.