They put weight on either the rims or the spokes near the rim.
Call some shops and ask about just balancing. You'll probably find out they either won't want to do it, or will charge the same as mount & balance, as they are accepting liability by taking on the work.
Prices will vary with the shop and how much business you bring to them. Most don't want to cater to skinflints.
If you should decide on inch size tires, many don't stock them as they are slow moving merchandise. If you deal locally, they will order ahead of time and may give you a break on mount and balance, including it int eh purchase price. You are trading off rock bottom price for having them mount and balance for you. It is usually cheaper to bring wheel to them, which they usually don't mind. That is certainly cheaper for both of you, rather than having them take the wheel off the bike and reinstalling it, too.
You probably should dismount and remount the tire on your existing rims just for the experience. It will make you appreciate what you are paying for at the shop. And, it is good to know how to do it if you are out in some desolate place and are forced to fix the tire or walk.
If you have a good shop in your area, it is worthwhile to build up a rapport with them. If they know there is future business, they will be more likely to offer deals. They get pretty good at spotting those that just take without any thought to their profitability, or expense of doing business.
