I don't know the answer to whether they will be open over the weekend, but i would imagine they would be. If it's any help, this is the link to the website but it is only in French or Arabic. There is an email address on it though so you may be able to contact them and check if no one comes up with the answer for you:
I did this journey recently and it was quite pleasant. I do suggest you book your tickets at the earliest though as it does seeem to be a busy service. One wise piece of advice given to me before I went was to book my return journey as soon as I got to Essaouira which I duly did. I met others who were struggeling to get seats on the day they planned to return because they'd left it late. Also, something I hadn't been told was that you have to get a seperate ticket for any bagage going into the hold. You get this from a seperate office to the ticket office and have to get it just before travel. From Marrakech it was 10dh per bag but strangely from Essaouria it was only 5h!
Have a great trip. I've not done an overview of my visit to Marrakech or Essaouria but I have done a number of reviews for places to eat etc for both which may be of help or interest.