Use 'sit tight' when you need to wait, especially if there's a delay or nothing else can be done. The flight is delayed due to the storm, so we'll just have to sit tight.
Pro Tip 2/3
No Immediate Action
'Sit tight' suggests remaining calm and patient, without taking immediate action. There's a power outage; just sit tight until the lights come back on.
Pro Tip 3/3
Temporarily Static
It often points to a temporary state where one stays put or inactive for a while. Sit tight until I return with more instructions.