If you are just now joining in on the process of making blackberry wine from fresh blackberries (preferably just picked), you can read about Part I here.
Taking off from where I left off, after letting the wine sit unmolested for a week, now is the time to drain off the wine must, add some more sugar syrup and let it burble some more.
5 1/3 ounces water
4 ounces sugar (about 3/4 cup)
Bring water and sugar to boiling and heat until sugar goes into the solution. Let the sugar syrup cool to room temperature (below 100 degrees F).
While the sugar syrup is cooling, remove the cloth from the container where the blackberries have been resting. Strain the blackberries through cheesecloth into a sterilized container, squeezing out as much of the juice as possible. Add the cooled sugar syrup and mix thoroughly. If you are reusing the original container, clean and sterilize before pouring the blackberry wine back in.
There are a few options for creating the right environment at this point. Many people will stuff wool into the neck of the bottle to allow the bubbling to escape, but prevent contamination. Others will use a balloon, but I can't recommend that method as several others have complained that it imparts a rubber taste to the wine, and you probably don't want that.
I had an airlock for when I was attempting the hard apple cider in the past. It didn't fit the neck (it was too small), so I retrofitted the airlock by cutting the original cap for the milk bottle a little smaller that the airlock and pushed it in that way. I'm hoping this is providing a good seal, but I guess I'll find out soon.
Let the blackberry wine (sans its solids) bubble away for ten days and then come back and check here for Part III of how to make blackberry wine. The next step involves bottling the wine, so if you are making it, you'll want to come here first to make sure you have all the equipment ahead of time.