rear sight out of plumb

[chaneylake]

here is how I checked tang site for plumb

1st I leveled barrel from chamber to front site
2nd I placed a level on barrel perpendicular aka cross ways
3rd I hung a plumb line about 24 feet from rear tang sight
with tang sight bottomed out I positioned it on plumb string and proceeded to raise rear sight
I did this 3 times on Saturday and once on Sunday morning and rear tang sight appears to be plumb with the barrel

from the bench firing at 100 yards with windage set on "zero" I fired 2 groups of 10, these groups averaged 1.9" to the right of center of bullseye

I then fired 2 groups of 10 at 200 yards, these groups averaged 6.9" to the right of bullseye

there was a very light incoming wind at about 10:30 at a maximum of 2-3mph, wind was so light that tree limbs were not moving and you had to look at tall grass to see if it was even blowing

my question is this, if the rear sight is plumb shouldn't the 200 yard groups be only 4" to the right of center if all conditions stayed the same