I can get the general idea of this phrase "as well he might" through the context, but I'm not sure I can explain it to my student. I don't have the exact text, but it is discussing political issues in regards to a particular foreign candidate and local crime.
Next, they use the phrase "as well he might" and continue with the statistics on the country's crime rate.
Specifically, my student is wondering how this is different from "he might as well".
Thank you for your help.
I think the clearest way to answer these questions about "What is the difference between two words or phrases that sound similar" is to explain that they
are different in meaning; to explain the meaning of each word or phrase; and to let the student decide whether the difference or similarity in meaning is worth noting.
(For example, this is how I'd approach the question of the difference between a cabbage and a carriage).
Anyhow, they are both idiomatic and it's probably not right to dissect them word by word.
"As well he might" means, "It would be well/good if he did". The speaker is asserting that a hypothetical action would be better if made reality - that he should do it. "As well he might" = "And so he should".
"He might as well" has at least two somwhat contradictory meanings:
i) "Nothing is lost by his doing it, and perhaps there is something to be gained."
Eg. "Since I'm going to London during the Olympics, I might as well visit some events."
ii) It can mean, "Nothing is to be gained by doing it."
Eg. "He wants the crime rate to drop without increasing police numbers. He might as well wish for snow in summer."
[Note: this is off the cuff, and probably not comprehensive.]
