More than one-third of Americans are now overweight or obese, due in part to a lack of access to nutritious, affordable food. Employers are feeling the burden, as they're often the ones strapped with the skyrocketing health costs.

Some health experts say Amazon is in the perfect position to help the situation.

The company has owned Whole Foods for almost a year and is starting to mark down the price of fresh produce. It has a relationship with millions of consumers through Prime, and will increasingly know about their health conditions as food becomes a bigger part of the business.

And Amazon has expressed a clear interest in improving workers' health and bringing down costs through its partnership with J.P. Morgan and Berkshire Hathaway.

"Amazon could do one of two things when it comes to food," said Jason Langheier, CEO of Zipongo, a start-up that works with large employers to help them promote and subsidize healthy food. "There's the home run, and then there's the incremental move."

The most ambitious option, Langheier said, is for Amazon to start by developing a web-based portal for its own employees, as well as for people who work at JPMorgan and Berkshire. There the company can promote meal kits, meal plans, recipes, grocery delivery options and even subsidies on fresh groceries for people at risk or suffering from a chronic disease like hypertension or diabetes.