One job I didn't do myself was bushings and seals on my 1100 Standard. Took them into a suspension specialist for the overhaul. I have Progressive springs, which I installed a few years ago. Upon picking up the forks, the guy told me to use a 10W-15 in the left fork and a 7W in the right. I put full synthetic fork oil of those grades in.
The technical reasoning behind the two weights mostly escapes me now, but each fork does a different job, as evidenced by a damping rod in only the right fork, so the different viscosities suit each fork's purpose better. The Honda manual does not make this distinction however, so I assume the functional difference is not really that viscosity sensitive.
However, I did use the different weights and I can't say it seems to make any difference.