"Stand by your man" is the name of a famous song (Tammy Wynette?). "Stand by me" is another one. It isn't just regional. "They stood by me when the going got rough" or "They stood by when the game got rough" are common comments. "They stood by and idly watched as the bully stomped the bystander" would be a legit comment.
Can someone tell me if this is right?
Стоять / постоять - to stand, to be standing, to stand (for some time)
Ставить / поставить - to stand up (someone or something)
Становиться / стать - to stand up (one's self), to become or begin something
Встать / вставать - to get up, to stand up, not really sure how it's different than становиться