Okay, with the proviso that I haven't actually read the study in question (only the abstract), it would appear that the results are based on simple correlations between BMI and cause of death.

All of the conditions that overweight allegedly "protects" you from are conditions that themselves cause weight loss! So, it's not that overweight protects you from tuberculosis, it's that anybody who does of tuberculosis usually loses a ton of weight before dying. Any serious, uncontrolled infection generally causes weight loss. Ditto for cancer. Ditto for emphysema (people burn lots of calories due to the metabolic costs of laboured breathing.)

Severe Alzheimers and Parkinsons also cause weight loss because the afflicted are unable to feed and care for themselves.

Unfortunately, the growing trend in medical journals is to publish any study that boasts large enough numbers without any consideration of the scientific merit behind them.

This thing should have been published in the journal "Duh".