The softer the stringbed the more forgiving the racket feels. Whether you want to get the softer from lowering the overall tension or varying the tension of different strings doesn't make any difference. The tighter the strings the less forgiving the racket is especially on off center shots. I think as your racket head speed increases you want to increase tension or use stiffer strings and vice a versa. As far as making the sweet spot larger or smaller I think there isn't a difference.
To make the sweet spot larger you have to start adding more mass. I do think the sweet spot moves toward any may that is added. Adding weight at the tip moves the sweet spot up and since the racket gets narrower the sweet spot gets smaller as it moves up. Adding weight all around the racket moves the sweet spot in all directions making it larger.
I would like to apologize to anyone I have not offended. Please be patient I will get to you shortly.