If the intention was to use a somewhat heavier lens, e.g. the 80-200mm f/4 AIS (810g) or 180mm f/2.8 ED AIS (880g), will a lighter weight body (e.g. the FM2N, FM3A, FE2) cause issues with regard to balance and strain on the lens mount compared to a heavier body such as the F100, F3, F4, F5 etc?
If the lens is big enough to cause too much strain on the bayonet it will most likely have a tripod mount of its own. So if it comes without one it is usually OK (not a rule withou exceptions but basically true)
Don't worry about the weight of the camera, I would not hesitate to mount any of these lenses on a FM2-3.
Usually a heavier lens vibrates less than a light one, so it can oftne be an advantage with a heavy lens (with or without tripod).
Why would you worry about the weight straining the mount? You should be carrying the outfit by the lens to begin with. when shooting, the lens should be cradled in your left hand, supporting all the weight. If the lens/camera combo is that heavy, you would never just suspend it around your neck by just the strap. When on a tripod, is the only time I would be concerned. There is a mount that can be purchased, that allows the mount to cradle both camera and lens, moving the balance point to the center of the combo.