Leather slings are heavy, esp the cobras. Maybe a big deal, maybe not.
True, most are, especially those that are wide. But my 1" Montana Sling is not much heavier than my nylon "Mountain Sling.
I initially bought a 1 1/4" Montana sling. Liked it well enough to buy a 2nd one later and went with the 1" sling the 2nd time. That is the only thing I use anymore.
The sling can be mounted in either direction. If mounted with the loop forward the loop can be utilized as a shooting sling. But I prefer to mount it with the loop at the rear. This places the rough-out leather against my shoulder and prevents it from slipping when carried. With the loop mounted forward you have the slick leather against your shoulder.
Personal preference and it depends on what is more important to you.