1.
If you wait up , you deliberately do not go to bed, especially because you are expecting someone to return home late at night.
I hope he doesn’t expect you to wait up for him...
Don’t wait up.
= stay up
PHRASAL VERB : V P for n , V P
2.
If you ask someone to wait up , you are asking them to go more slowly or to stop and wait for you. ( AM INFORMAL )
I was running down the hill shouting, ‘Michael, Michael, man, wait up’.
= wait
PHRASAL VERB : usu imper , V P