I am not sure about the overhead and additional cost of shorter sprint. In the book "Software in 30 days" by ken and Jeff ,there is a costing table of short vs long sprint.
where short sprint has a accelerated increase in cost with decrease in sprint size.I am confused about the costing as the events in scrum scale linearly.(for example: sprint review is for 4 hours for 4 weeks sprint and for 2 hours for 2 weeks sprint).How short sprints has more overhead than the long sprints.