modals for possibility

[bosun]

1. He could’ve gone to the movies. – possibility
2. He might’ve gone to the movies. – weaker possibility
3. He may have gone to the movies. – stronger possibility

Do above examples mean that could have gone mean the weakest possibility?

 

[5jj]

1. He could’ve gone to the movies. – possibility
2. He might’ve gone to the movies. – weaker possibility
3. He may have gone to the movies. – stronger possibility

Do above examples mean that could have gone means the weakest possibility?

No.

There is often no real difference between 'could have' and 'might have',

In your two sentences, there is perhaps no difference, though it is impossible to say without further context. In the following two sentences, there is a clear difference.

I don't know where John is. He might have gone to the movies, or he might have gone to the pub.

John was free yesterday evening, so he could have gone to the movies if he had wanted to, but he said he was too tired.

 

[bosun]

I am studying modals, but to me, could and might/may are very confusing. Some like you say there is no big difference, but depending on the context I find only ' could' is the right answer while might and may have the similar meaning. That's why I am posting similar questions, and nobody explained to me clearly the differences between might, could, and may.
For example,

What is my jaket? It should be in the closet, but I cannot find it. Where could it be?
Here, I think in terms of meaning might and may are possible answers, but some people say that only ' could' is the right answer. I don't know why.

 

[Raymott]

I am studying modals, but to me, could and might/may are very confusing. Some like you say there is no big difference, but depending on the context I find only ' could' is the right answer while might and may have the similar meaning. That's why I am posting similar questions, and nobody explained to me clearly the differences between might, could, and may.
For example,

What is my jaket? It should be in the closet, but I cannot find it. Where could it be?
Here, I think in terms of meaning might and may are possible answers, but some people say that only ' could' is the right answer. I don't know why.

You need to understand that there is no inherent difference in probabilities. That's not a function of using "might" over "could" or vice versa. On the other hand, they are different verbs with different meanings.
So to assume that 5jj is saying that there is "no big difference" in the terms is wrong. Sometimes there is no difference in meaning at all, and sometimes there is a big difference; you can't average that out and say there is "no big difference" between the terms.

With your jacket example, you could ask yourself, "Where might it be?" You can't ask, "Where may it be?"
Unfortunately, some people might/do say, "It may be in the cupboard" (meaning 'might'). This is generally accepted. But you can't ask, "May it be in the cupboard?"

You might/could/may also benefit from searching this forum for these terms and reading the voluminous posts on this.

 

[5jj]

That's why I am posting similar questions, and nobody explained to me clearly the differences between might, could, and may.

The reason is that there is not always a clear difference.

When there is a clear implication of ability, then only can and could are appropriate; when it is just a question of possibility, then may, might, could and (sometimes) can are all possible choices.

Things are complicated by the fact that, for some speakers, might expresses a more remote possibility than may; others use the two words synonymously; others do not use may at all. This is why you will get different answers.