No one here can answer your question since there is no set/predictable schedule for Double XP Weekends. At this point in time, you're better off playing the game normally and saving your XP if you're waiting for double to use them.
Generally around 6 or 7 months between double xp weekends. That's all tied to whatever episodes or content they are adding up and want to drain the reserves before rolling out the new must have artifact. Good rule of thumb is to think of all the different type of bonus weekends they like to do, and expect to have most of those twice before it's double xp again. My guess is late March at the earliest, but I'd welcome a surprise.
Actually, I've been able to predict it. We will get double marks weeked for all content except current episode in around 2 weeks from this thursday. 2-3 weeks after that, we will get double or triple mark weekend for only current episode. It's done that way for the past 3 Episodes.
Except that's right around/after the holidays. Not a whole lot happens once you get around the 24th, unless it's a server emergency kind of thing.
He's asking about double xp though. Double or triple marks are are almost pretty much expected. I think we only get double XP twice a year, can't recall off-hand.
You are able to predict it... except we aren't sure you're right and those are all specifically not what they were asking about.