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It is from this article. Here it is:

Some is good, even downright healthy, but too much could very well be a problem.

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very well (idiom): 2: reasonably or properly, I can't very well show up at the wedding uninvited.

In your example it's just an expression synonymous with "reasonably". It's often used with conditionals to indicate plausibility. Other examples:

Although the weather forecast says it's going to be clear, it very well might rain tomorrow, so bring your umbrella.

Our team could very well take the title this year.

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