"I weigh sixty-three kilos."
Translation:אני שוקל שישים ושלוש קילו.
For numbers of things above 10, there are two patterns that are "allowed": gender-agreeing number and the noun is plural, or counting number - which is always in the feminine form - and the noun in singular. Examples are: שנים עשר שקלים / שתים עשרה שקל, עשרים ושלושה אנשים / עשרים ושלוש איש, שישים ושלושה קילוגרמים / שישים ושלוש קילו(גרם).
Note that this form is not commonly used with every noun. It's very common with currency and with measurement units, but other than that you are safer with the "normal" form.
I do not know of this form Only the noun can be changed between singular and plural forms, while the number has to agree.