'Might' was originally a past tense of the auxiliary verb 'may'.
It was particularly useful in reporting speech, where the reporting verb was in past tense.
e.g. : He said that he might come.
The reporting verb 'said' is in past tense. The verb in the reported clause 'may' , became 'might'.
Question : What is the implication of 'Might' as a modal verb?
'Might' indicates 'a probability of 50% , a la its basic form 'may'.
We can use the analogy of 'a coin tossed into the sky' , to estimate the implications of 'might' or 'may'.
A coin thrown into the sky , say a 100 times, when it (coin) falls may show up 50 times heads and 50 times tails, with about a 10% deviation on either side.
He 'may come' - this sentence carries an implication that he 'may not come' . It indicates a near 50% probability on either side.
Question : Is it reasonable to say 'He might come'?
This usage is quite common and it has become acceptable.
The present tense form of 'may' seems more appropriate, because the event (of his coming) is yet to take place.
Question : Can 'might' be used in simple past tense?
This is taking place in reported speech (indirect speech).
Example : He said that he might come. (Past tense).
Example : He says that he may come (Present tense).
It is difficult to trace a stand alone usage for the 'might' past tense usage. We can see the 'present perfect tense usage' everywhere:
Example : He might have come.
This sentence augurs well with the implication of 50% probability of the event in the immediate past. The speaker is estimating/forecasting/guessing.
Question : Is it reasonable to say 'Might you try some coffee?'
We can find some current usage.
The speaker seems to intend a 50% probability.
Use of 'might' as a form of past tense , has been given a 'bye'.
We can probably use : 'May you please try some coffee?' .
But, some interpreters say that use of 'may' in seeking permissions is too formal.
Question : Doesn't 'might' mean ability and power?
We can say that there are two mights. This 'might' , we can call 'might 2'.
Example : Money is might.
Question : Is it reasonable to say 'It might rain tomorrow?'
It may be difficult for us to accept this usage, if we go by the literal interpretations that 'might' refers to past tense and 'tomorrow' refers to future tense.
The usage has come to stay.
Some grammarians say that 'It might rain tomorrow' is less positive than 'It may rain tomorrow'. Can we say that this interpretation implies: 'It may rain' refers to a 50% probability and 'it might rain' refers to a 40% probability?
Question : Is it reasonable to say 'You might pay a little attention to your weight.' ?
Some grammarians say that 'might' can be used to convey 'a degree of dissatisfaction'.
The usage has come to stay.
I, personally prefer the usage 'You may please pay....' construction.
Modal verbs are supporting verbs (also called auxiliary verbs). They indicate the manner in which the speaker intends the action of the verb used by him is to have its effect. The verb may indicate a duty, ethical obligation, possibility, impossibility, probability, necessity, compulsiveness etc.