I don't think we have to write in spoilers, since the episode is out on Youtube now. I don't think the guard that are told she is grounded are there to stop her like a real prisoner. Imagine it was you and your parents grounded you and told you you can't leave the house. Going against that isn't a great physical feat, you could easily she run out the door or climb out the window. But it would get you in even more trouble with your parents. In Weiss' case, she already proved that an army of Atlas soldiers (or White Fang members) can't stand in her way, but her father would probably outright outcast her to "protect" the Schnee name and maybe some of these social threats are what holds her back.
Yeah but...I don't think she was asking for her father's permission when she told him she wanted to leave. The way she said it was less of a "Can I leave" and more of a "I'm leaving". Like she could honestly care less if he approved or not (which made her shock over losing her birthright all the more confusing. What did she think was gonna happen if she left?)
And then he slapped her and all of a sudden she went into submissive prisoner mode.