Are plebe allowed to go out on the weekends? And how is it with leaving and going home on a weekend if you live close?
In recent years, plebes have been allowed Town Liberty (can leave Yard) on Saturdays, until midnight. There are regulations on how far you can go, but if your family is close, that is something you can figure out with your chain of command once the ac year starts. When plebes get cut loose on Sat depends what has been scheduled for Sat AM, and anything pending the plebes have been tasked to do. If you have "the duty," you cannot leave the Yard. There are also restrictions on who you can be in a POV (privately owned vehicle) with: parents, sponsors, commissioned officers, etc. Not civilian friends.
Sunday, you have Yard Liberty. You can't leave, but people can visit you in designated areas.
Overnights/weekends away - you will learn what you rate and what you can earn.
Of course, during PS, you don't leave the Yard on Town Liberty until PPW.
During the ac year, you will have a lot on your plate, and to your surprise, will find yourself self-limiting your liberty so you can keep up.
The amount of Town Liberty increases each year.
I encourage you to browse through the USNA forum, where you can read about much of this.
It's all in USNA Midshipman Regulations, various editions of which can be found online. That's only if you are hardcore...
I am sure a current mid can amplify.