The design in question here is an official variation of the SBI logo:
Now, I’ve always felt that the main circular icon feels a bit smaller, and must be corrected by enlarging it a bit to make it look more aesthetic and balanced from both sides. I’ve seen many many famous designs that do things like this, just to make it look better, so I guess there must be some reason behind it.
Am I correct and if yes, what is the reason for this?
In typography, this is called an overshoot. And has been a very long-standing practice.
In typeface design, the overshoot of a round or pointed letter (like O or A) is the degree to which it extends higher or lower than a comparably sized “flat” letter (like X or H), to achieve an optical effect of being the same size; it compensates for inaccuracies in human visual perception.
Yes, it makes a difference. Human visual perception is not always a mathematical constant.