What you have is a ladder peep sight on the 1903-A3 the numbers are your elevation adjustment going from 200 to 800 yds as the U.S. military unlike the Europeans trained soldiers and marines in long range marksmanship. By moving the rear peep back it adjusts the elevation of your line of sight. There's also a knob to the right and numbers on the rear of the sight. This is your wind-age adjustment which can be moved right or left. When I was a young Marine we called this doping your weapon. The 1903 with those sights is an extremely accurate rifle there were reports in WW1 that soldiers and marines were dropping enemy soldiers at distances out to 800 yds with these rifles. You have a great piece of history there I hope this helps you out.

I looked at a nice one 1903 a couple days ago. Great condition on the outside but the bore was gone due to corrosive primers. $800.00 and the owner was not budging. Wow.