You are correct in observing that Spirit and many other airlines do not publish a specific weight limit for carry on bags. Probably because this is a limit there's hasn't been a notable reason to enforce. Some exceptions are described here.
The most specific practical limit you must comply with is any limit of the overhead bin. I don't know what they generally are, but I've seen the stickers and some posts indicate 70-90 lbs. The workaround for that is to put the bag under the seat in front of you.
10kg is not particularly heavy, but at the upper end of the above limits. Note, while it will likely go unnoticed, if the crew does notice and thinks it might be to heavy to be safe, they will require you check it. Once that decision is made, there is no point in arguing. You only options are check the bag or depart the aircraft.