Even Greener Pastures

I came across this the other day
I'd like to know how native speakers see it. Would you use could, may and might in different situations, to express different degrees of certainty, or do you see them as interchangeable?

The example is about something that could/may/might happen in the future:

The restaurant may close.
The restaurant could close.
The restaurant might close.

It also says that the speaker shows degree of certainty by stressing either the modal verb (meaning they're less certain) or the main verb (if they're more certain).

The restaurant might close = less certain than The restaurant might close.

At least in the example sentences you gave, "may" seems to express a slightly more remote possibility than "might", but it also sounds more formal; "might" is much more common in colloquial speech. With "could", I'd be more likely to expect a conditional clause to go with it, e.g. "The restaurant could close if they find out what you've been putting in the soup". Those aren't hard and fast rules, though, and I'd say you could usually get away with using them interchangeably.
The bit about stressing the modal or the main verb is correct.

Thank you all for your feedback so far.

Coligno, this is interesting because according to the source I mentioned above, may should be the most likely of them all. That's the exact opposite of how you feel about it. Mind you, it does also say "Many native speakers disagree on which one expresses more or less certainty."
Regarding may being more formal, I keep hearing this but I've heard it used quite a lot in informal speech (we're talking about the may that indicates certainty, not the may you would use in a polite question), especially with "well".
"It may well close down."
"It may well be that we'll have to find another place."
But then again, does well mean I'm more certain?

Where I am from ¨may¨ is not more probable than ¨might.¨ All of those depend on context and tone of voice for the listening to make a judgment about the probabilities.