What do you mean by "not too tight? Is it the main body of the shell not tight in the chamber or is the rim of the brass not tight where it seats at the chamber ring or throat?
With a lot of gauges, there is a bit of leeway allowed in bore dimensions. Also, a shell is not always "tight" in the chamber. A shell that is quite tight before firing will often have trouble ejecting. Below is a reference to 10.6 mm markings.
But to clarify--is it a shotgun or does it have rifling?
3 - France, in 1810, try to get away from the british system and they managed to keep alive two systems: one was similar to the British (except the french pound was different) and determined gauges fairly similar in diameter to the british system;
the other, called the bore system, was similar, but used the kilogram (for example a 32 bore was very similar to a 12 gauge).
In 1868, they killed the bore system and tried to rationalize the dimensions. They still based the determination of the gauge on the number of lead balls made with a french pound, but they decided to adjust the diameters to have 0.2mm steps between gauges.
This is probably were the .410 was born (even though was not called so; officially it was called a 12mm):
in fact, the french proof house decided that all the guns smaller than 10.6mm (roughly .410") had to be tested for pressure in a different way than the bigger ones. So, .410 became the divider between serious guns and play things.