According to the dime book the overdate makes up about 45% of all the 1798 dimes. (About 10% of those are the JR-2 variety)
The 16 stare only comes on the overdate, but the overdate comes with both 16 and 13 star reverses.
You might say the size of the 8 had a bearing. The overdate was a dated but unused 1797 die that had the small 8 punched in over the 7. Since the second obverse has the same large first 7 and the same small 8 most likely it was a leftover die created in 1797 but not fully dated. (This was common practice. Make up the dies in batches but leave off the last digit of the date so that when the die was going to be needed the correct last digit could be punched in and the die hardened. This was done to try and avoid having unused DATED dies leftover at the end of the year.) The third die not only has the large 8 but it also uses a different smaller sized 7. This die was probably created in 1798.
The 16 star reverse was also a leftover die from 1797. It had been retired from 1797 quarter eagle production and it was paired with the other leftover overdated 1797 die until it was retired for good. So you could say the size of the 8 had a bearing because they decided to use up the left over dies first.