@tppm
originally the mass of one cubic centimeter of pure water at three degrees Celsius
IIRC, originally intended to be the mass of one cubic centimeter of pure water at maximum density (about four degrees Celsius), but they were out by about 28ppm - even then, defined by cubic decimeter and kilogram.
The unit system is meter-kilogram-second, even though (as you say) kilogram is not a base measurement (although it is the reference standard). Prior to that, it was centimeter-gram-second, again with a non-base unit - and with two of the units not matching the reference standards (meter and kilogram). Before that, in a lot of the world, foot-pound-second. But then, the meter is now and a second was defined as an arbitrary number of wavelengths/oscillations of given light - and not even the same light!
The standards are chosen for relative ease of laboratory reproduction, to match historic prototype standards which had limited accessibility, and those standards were chosen to be a useful size - a standard of one gram would require a much more precise balance than for 1kg, and most real-world uses would require multiplying up to kg-scale anyway.
BTW, degrees centigrade are defined from the temperature in Kelvin, which is set from the triple point of water (0.01 deg.C), again chosen to make the new definition match the historical units. Even the historical freezing-and-boiling water temperatures, subject to small variances due to air pressure as they were, were quite a bit more sensible than defining 'zero' as the lowest temperature found by adding various salts to ice, and 100 as body temperature. {add] Though, that's just like defining 'inch' as the width of a thumb, foot likewise, etc.