Why is the N-number on the tail of aircraft sometimes shown in both large and small font?
The N-Number marking regulations are outlined in this AC for fixed wing aircraft:


  ... minimum height of 12 inches
  
  (1) On both surfaces of a single vertical tail or on the outer
  surfaces of a multi-vertical tail, or 
  
  (2) On the fuselage surfaces, on
  both sides of the fuselage between the trailing edge of the wing and
  the leading edge of the horizontal stabilizer. If engine pods or other
  equipment are located in this area and are an integral part of the
  fuselage side surfaces, you may place the marks on those pods or
  equipment.


However for some time 2 inch markings were allowed:


  On an aircraft displaying 2-inch marks before November 1, 1981, and on
  aircraft manufactured between November 2, 1981, and January 1, 1983,
  you may display those marks until the aircraft is repainted or the
  marks are repainted, restored, or changed. Once the aircraft is
  repainted or the marks are repainted, restored, or changed, the
  N-number is required to be 12 inches high.


Its possible the numbers you are seeing are the old ones and the new 12 inch numbers were applied directly beneath it to comply with the new marking regulations while the old ones were simply not removed.