Hi all,
On the military versions of the B737, for AEW&C and MMA, the eyebrow windows will be used during the maneuvering for air-to-air refueling, though when the airplane is approaching and in the correct position, the pilot can see the line-up points and fuel boom through his main #1 window.
The eyebrow windows are needed to increase visual coverage to suit any eventually.
FD