grammar

It may be determined by tangibility. An object as a book or knife, you could say "give it to me"; whereas intangible things such as answers, or ideas, "give me it" would be appropriate. But, if there is a question a choice of receivers, "give it to me" would be used, unless it was an order, or imperative, than "give me it" would be more correct. IMHO

Jack, well put!

You fellas don't need me

Your idea, while intriguing, Jack, doesn't match actual usage.

Both are correct and these two forms are used for a limited set of English verbs. There are a number of observations made about the two by language scientists but they escape me at present.

It's jack.

I prefer "give it to me baby uhuh uhuh" but in less formal settings I might condescend to use "gimme it" or the imperative "gimme".

You're really croakin' there, Missy.

Just licky, thanks JTT. I love the way you create a mood so palpable that even those that will not see can almost touch it.

"Give me it" is still pretty common, esp with emphasis on "Give". So Mili I inquired of my Better Half, who is much smarter than I, and she replied "You'd be more likely to say 'Give me it' to a small child or dog"