"Let's give it up for..." Strange idioms..

This particular phrase irritates me; I don't know why. But here's how it is used these days. Let's say I'm at a conference, and the speaker or panel is wrapping up. Then the moderator comes out and asks you to 
​"Give it up for--today's speaker, Suzie Q." Of course, that speaker deserves a round of applause. But where did that phrase come from? And why does it mean, "Let's clap for" or "Let's give a round of applause for" the speaker? ​

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The first time I heard the phrase was at an innovation conference in 2006 I think. The speaker had just wrapped up his presentation. Then a colleague of mine, an academic, came bounding out on stage to thank the speaker. He loudly announced, "Give it up for our great speaker." At first I wondered, "Give what up for the speaker?" But then when everyone started clapping, I understood. And joined in.  But I was still puzzled. The phrase did not seem connected to what was being asked of the audience. So like any good etymologist, I researched the origin of the phrase. It was hard. In fact, I sort of came up empty until I ran across one explanation that seemed strangely feasible to me. I'll share it with you.

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The OED (Oxford English Dictionary) traces the use of the word "give" in related expressions back over 1000 years. It suggests that this expression of gratitude somehow originated in the time of Beowulf. As semi-proof of this, the OED cites a sentence which I'll give here in translation: The poem says of Heremond, a Danish King , "Not at all rings did he give to the Danes for honor." That means that he didn't "give the rings (up) to his men" as a reward for their service"...Well, that could be a connection to the phrase as we use it now.   

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But then the OED sort of reversed itself and added to the puzzle. The OED points out that the first modern usage of the phrase it was in 1990. So even these experts don't understand why an audience is asked "to give something up" -- rather than "give something to" the speaker after he or she speaks...