Q: What is the Stalker speed increase? When using Stalker, I feel that I move faster aiming down sight than walking normally.
Is this true? Also, in objectively relative terms, what is the speed advantage from using Stalker? 

A: With Stalker, you do move faster while aiming down your sights than aiming down your sights if you didn't have the perk. When you upgrade it to "Pro," it also delays triggers, such as claymores, (similar to Scrambler Pro, MW2).
However, you move slower when you are aiming down your sights, no matter what.
The best way to figure out the speed advantage would be to have two people, one with, one without Stalker, have a "running race," while aiming down their sights, and see how far one can get before the other, as there have been no official numbers released yet!
Source:
Call of Duty Wiki

A: You move at the same speed as when you're not aiming down the sights.
The reason you perceive yourself to be moving faster is because of the increased level of zoom you're now viewing the world at.
