In general this has more implications than simple singular/plural forms of units. Agreement/concord/congruence is the proper term. In some language you will even change the form given the distance to the thing you are measuring or counting, even depending on the type of thing you are measuring or counting, or change on the gender of the thing, and then even only for some numbers.
Now assume "kilogram" is changed to the short form "kilo", then it is "én kilo" which is masculinum. The prefix "kilo" is only used for "kilogram", so it isn't valid Norwegian til say "én kilo" when referring to "1 km", or "én milli" when refering to "1 milligram".