The short answer to this question is that it's cheaper to move on a Monday, Tuesday, Wednesday, or Thursday from Monday to Friday. Simply put, most moving companies offer better rates during the week because they're not as busy at the time. Turns out, the best days to move are between Monday and Thursday, even though Tuesdays are the least popular day to move. There's much less demand for moving, so it's very easy to schedule the moving day, and taking the day off to do so will pay off to a great extent.
You're likely to save money by hiring a moving company during this strange part of the week when no one else moves, and you'll have the whole weekend to pack your bags and get organized before the workweek.