I agree with Ben: it means he was very tired. The "not" reverses "a little"... therefore, "very".
You'll see this negated form used in order to convey the meaning indirectly.
"That was a stupid thing to say." (direct) - "That wasn't a very intelligent thing to say." (indirect)
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It means "He is very tired."
"Not a little" means "very; very much; a great deal of".
It is standard usage and perfectly correct grammar.
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Hi Ruby,
Its actually not good grammar..and really depends on the context. But it would usually be a way of emphasizing that he WAS tired!
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We need more information. It sounds like the person "was not even a little tired" meaning they were wide awake
It is possible that they could say "He was not a little tired, but very tired!" However they would probably make it more obvious if that were the case. (I'm guessing it means they were wide awake)
Hope this helped!