Fasnap said a "sheet of paper" thickness? that is .1mm. point. one. mm. anything that thin which I'm guessing is dramatized, or even close to that thickness I wouldn't consider "heavy duty"
Lord & Hodge grommets are the type that the male end is hammered and curled to lock in the washer, it is pretty thin, but not paper thin. I'd say about the thickness of a nickel. It takes me a good 15 to 30 secs of hammering to get it set so that tells you the weight of the metal. I'm guessing you have a kick press or hand press to set so you can prob get it slimmer than I can. Ive used them with heavy canvas, 12 - 14 oz. and leather around the 8 - 9 oz range. Never any problems.
IMHO self piercing will prob give you more issues than convenience. I can imagine the leather pulling around the circle leaving creases as it tries to pierce the leather, perhaps even making the hole a touch larger than the fitting, which will end up pulling out over time.
Have you thought about eyelets instead? Kinda the same as a grommet but typically smaller and thinner, used as reinforcement, the same as a grommet, but a bit more "decretive" because the eyelet has a flatter and more "attractive" flange. Not sure what your end use for the hole is but a good rule of thumb for use between is: Eyelets are used to reinforce the hole and protect the material it incases, while grommets do the same with the added benefit of reinforcing the stress placed on the hole from attachments to it, like a snap hook.
Just my 2 cents.