Are cloth simulations affected by scene units? I am working on a character scene and I want them to have dynamic clothing. While working on this I suddenly realized that the character is gigantic in scene units, about 47 feet high! The cloth simulation is acting a bit "light", as if it were made of tissue paper, but it is not slow. I would like to verify whether cloth simulations act differently based on the size of the object in the scene, or if i just need to change some settings to make the cloth have more weight and to wrinkle less (I am going for a leather type material). 

Scaling the scene down to real-world size is not an option because it breaks self-collisions in the cloth, as some of the geometry is below the minimum distance I can set the self-collision distance to, causing the cloth to "explode".

Sorry if this a noob question but I am very new to cloth simulation in Blender and don't know what all the settings do.
Yes - size will significantly affect all of the physics simulations. Of particular interest will be the acceleration due to gravity; by having a 10x too large scene you are effectively applying only 1/10th of the force of gravity (which could explain the tissue-paper behaviour of your cloth).
Quick solution would be to adjust the scene gravity by a suitable factor to account for your increased scale (eg, change from -9.8m/s to -98m/s for a 10x change in scale). However, you might still get it behaving a bit oddly since any stiffness and weight will be similarly affected by the scale.