If this is a date or a prearranged meeting, you can be sure he likes you and is there for you. This is totally appropriate behavior for a lady being escorted by a gentleman at any age.
It will make him feel like a man and will initiate physical contact.
School or the restaurant where all of his friends hang out are not.
Young guys are often very nervous about public displays of affection, so make sure the setting is comfortable for him. Romance is not a manly thing in the slowly-maturing mind of a young man.
If he responds to your touch with his hand, take that as an invitation to give him your full hand.