To stay up is to keep yourself awake past your usual bedtime. Stay up late, stay up for the results, let the children stay up.
It always implies a choice, which is what separates it from lying awake. The thing you stay up for takes for, and the lateness takes late.
1phrasestay upTo keep yourself awake past your usual bedtime.
“They let the children stay up for the fireworks.”
stay up is a phrase.
Practised in Phrasal Verbs