Stress causes cortisol to be realeased from the adrenal glands. When cortisol levels are chronically elevated, many harmful effects on the the body can occur. The most prevalent of these include weight gain, decreased immune function,  and a higher risk of chronic disease.

Here is an example of how the stress response occurs in the body:

1. An individual becomes stressed 

2. A complex hormonal chain-reaction begins, and the adrenal glands secrete cortisol

3. This prepares the body for a "Fight-Or-Flight" response by flooding the system with glucose

4. Insulin production is inhibited by cortisol's secretion, and blood sugar levels increase

5. This can lead to glucose-starved cells sending "hungry" signals to the brain, overeating, and excess glucose being stored as fat in the body (especially as visceral fat around the organs).

*Source linked here

Simply put:

High blood-sugar levels become normal and cells in the body become more and more insulin resistant. Both of these factors contribute directly to weight gain and other health issues.

High cortisol levels are also believed to contribute to:

Gastrointestinal problems, fertility problems, insomnia, chronic fatigue syndrome, thyroid disorders, dementia, and depression.