I'll give it to you straight...

Let's look at some idioms with "give."

"I'll give it to you straight, Babcock. You lack the killer instinct."

Add the phrasal verb up, and this is what you get!

"Up" gives a sense of finality - of a change from one state to another.

To give your all means to use all the effort and strength that you have

How about the phrase "I'll give you that." It basically means "I concede the point" or "I admit that it's true." This is usually followed by "However..."