Do you use 个 when describing distances/weights？ I'm trying to figure out if you ever use 个 when describing distances or weight. For example, people say "十公里“ NOT "十个公里“ － right？ does the same apply for weights? like 公斤？
No, in general, you shall not use 个 before a unit, no matter what the unit is used for (mass, length,area etc ). 个 is a counter/measure word in Chinese, one of whose functions is to count something, like a unit, so you don't need to put a unit before a unit.
In some weird scenarios, you may use 个 before a unit.for example,


  本文中有几个公斤？ How many occurrences of "kilogram" in the article ?


Here, kilogram itself is treated as a common word instead of a unit.