To respond to the earlier comment, yes it's true that at one time I thought that 3 micron diaphragms were preferable for LDCs, and possibly a bit thinner for SDCs. I have since come to a different conclusion, that 6 micron is in general a better compromise, along the lines of the balances and tradeoffs that Klaus mentions. I had convinced myself that 3 micron was better, and worked for several years to produce repeatable and good sounding diaphragms with that material. When I reached what seemed to be a limit, I started working on 6 micron material (and everything else from around 0.4 micron to 12 or so) and found that 6 really did work out better for most mic designs. The differences are minor, once the stability issues are solved, and it really makes very little difference, within reason, because the dominant mass is not that of the diaphragm, but that of the air load on either side of it.
However we should be clear that the thickness is not the issue at all, it's the mass. Nickel weighs 6.4 times as much as mylar does per unit volume, so it's no surprise that a nickel diaphragm of about 1/6 that of an otherwise equivalent mylar diaphragm works out best. The nickel diaphragms on our C617SET omni microphone are 0.9 micron, made by Gefell the same way they were for the KM53/54/56 microphones. The equivalent mics from Bruel and Kjaer in years past were also nickel of the same thickness (now they are mostly rolled steel).