A gram is not the base unit, it started with one meter (hence, metric).
Kilo means thousand in Latin, so 1000 meters became one kilometer (aka, one thousand meters), and when they need smaller units, they took to Latin again, simply because the language was en vogue for science:
Deca (ten): Decimeter (dm, nowadays hardly used, but it exists) = 0.1m
Centum (hundred): Centimeter (cm) = 0.01m
Mille (thousand): milimiter (mm) 0.001m
Weights were then adopted from the dimensions based on practicality, i.e. one liter was a common enough volume that people could use it in a household, and it's defined by 1dm height x 1dm length x 1dm width. Or 10cm10cm10cm (same thing, but the base notation was units of one).