If you're looking for a meeting place or a good stop around ½ or halfway between Weimar and Berlin, you can try Wolfen, Germany, which is about 1½ hours northeast of Weimar, or about 1½ hours southwest of Berlin.
About ⅓ or a third of the way, you can stop at Bad Durrenberg, Germany. This is almost an hour northeast of Weimar.
If you drive straight through without stopping at all, the total distance is 285 km. The distances shown above don't include local roads to get into each town, so if you're planning a long road trip, make sure you factor in traffic and road conditions, rest stop breaks, and interesting detours along the way. If you're in a rush, you can do the trip with zero stops, and your total travel time would be around 3 hours, 3 minutes.