"How much do you weigh?"
This expression uses "to be" rather than "to have." It is different from the other stat question in the exercise: Boyun kaç? which means "how much is your height?" while Kaç kilosun(uz)? means "How heavy are you." The confusing part is that "Kilo" in Turkish is both a concrete noun (kilogram) and an abstract noun (weight), and context determines which it is.
Sure. The difference is the possessive suffix -un vs. the verbal suffix -sun(uz). (Remember that the verb "to be" is irregular - it is added as an unaccented suffix to adjectives and nouns). So with "kilo" it is just like the difference between "your cat" (kedin cf. kilon) and "you are a cat" (kedisin cf. kilosun).
The difference is actually more clear with second person (because possessive and to be are different) and less so with first person because they are spelled the same (patronúm - my boss vs. patrónum - I am a boss).