He is addressing her formally, so he uses the third person. In Spanish, there are three degrees of reverence:

Vos - this is extremely archaic and in most dialects, it is almost obsolete. Normally, it would be reserved for the uppermost aristocracy, royal families or the highest dignitaries, such as the Pope and Cardinals. Still, it isn't used anymore, with the exception of some Latin American variants (Argentina, Uruguay, Paraguay, working class people in Central Chile, Northern Peru, Ecuador, the Maracucho dialect in Venezuela, most of Central America from Nicaragua to Southern Mexico), which use it instead of the colloquial tú. Whenever this is used, the verb is conjugated in the second plural person.

Usted - from the 17th Century onwards, this became the standard manner of addressing those who are above us in the social scale, or merit particular respect. Whenever this is used, the verb is conjugated in the third singular person (as is the case with this song).

Tú - this is the standard way of addressing people at a colloquial / familiar level.

So yes, this would be the reason behind the way in which the lyrics to this song are written. Unfortunately, this is difficult to properly translate into English, as there aren't such evident ways of indicating reverence / status in the vernacular. Sorry for the lengthy explanation!

Have a lovely day :)