That does also depend on the era; on late Medieval battlefields armor was pretty ubiquitous.
Well, that isn't relevant to the use of leather for 'armor', because in that case it's just a costume isn't it? I mentioned the SCA gear because their kit is assumed to have some protective quality to it, at least against blunt impact, though again, I don't think leather actually holds up to sharp edges very well regardless of how thick it is.Larp is larger than just SCA though. Consider other organizations, like Dagorhir, and you can definitely see that the rules allow much cheaper/easier/lighter "armor" than metal. The larps for which combat is more of a tap sport are even less likely to require leather to be particularly thick.
Basically just trying to provide some context on the heaviness of leather as armor, the way it's depicted in RPG's. Obviously it can thin as you like for clothing or decoration (which is actually all armor usually is in most fantasy films and a lot of RPG's).
G