Two weeks is the exact timespan of the height of the Cuban Missile Crisis. On session one the players discover the missiles (literally or figuratively by analogy). In the intervening days they situation continues to escalate. On the final day they must step in and create some kind of solution.
If the sessions are two weeks apart, there are 13 days in-between. Perhaps a game based on superstition. You could have one session, then provide email updates on each of the following days until on the 13th day, something terrible happens. They players convene for the second session on the following day to deal with it. Or you could have 13 murders, each being described in emails one by one during the intervening days and in the second session the players convene to solve the mystery.
13 could represent the 13 founding colonies of the United States.
It is also close to a dozen so long as you figure out what to do with the extra day. Maybe some resolution having to do with one egg each day? (with the army major as the 13th)? (with the parents as the 13th)?
Thirteen is also a bakers dozen. Perhaps for resolution thirteen people must bake a baker's dozen of cookies and pass them around. Everyone eats one each day before the final session, and whoever made the best cookies gets some kind of in-game benefit.