"Stood up" or just "stood"

"Stand up" implies someone is sitting or crouching, then stands "up." But "stand" could work, too. "Stand" alone means the person just stands, as opposed to siting or crouching.

Mary asked him to stand [up].

Mary asked him to stand up from where he was sitting.

Mary asked him to stand over there.

It can be redundant, I think, but sometimes the extra syllable can be used for rhythm.

To me stood and stood up have totally different meanings.

He stood and extended his hand. (He got up from a sitting position and began the act of shaking hands.)

He stood up to her angry rant. (He refused to back down.)

The charges stood up in court. (They were verified as valid.)

[casual/slang] She was stood up by her date. (The date never showed up)

You're speaking of two different usages for the word.

First, "stood up" is perfectly good grammar.

The difference between "stood up" and "stood", to me, is action. "He stood in the doorway." vs "He stood up and stared at Marie." The second implies he had been sitting and shows action as he gets to his feet. The first suggest he could have been lurking in the doorway without moving for some time.

Oi.

He stood from his seat to greet her.

He stood up from his seat to greet her.

...

These are apt examples.