First, does your parish have enough priests and deacons to cover all the Masses? Sometimes that is a valid reason for allowing parishoners to preside over masses. Normally you are correct in the belief that only a priest or deacon could give a homily. In fact there are rare cases where priests have been ordained with the stipulation of not being able to give homilies or hear confessions such as Fr. Solanus Casey. However, in cases of hardships like not having enough clergy to cover all the Masses then qualified individuals like catechists, facilitators, etc. who are accustomed to leading prayer groups may lead a prayer service to satisfy Sunday obligation. Any homily, however should be submitted to a priest or deacon of the parish for review to insure that it doesn’t contradict any Church teachings. The quote below is from Canon Law.
§3 Where the needs of the Church require and ministers are not available, lay people, even though they are not lectors or acolytes, can supply certain of their functions, that is, exercise the ministry of the word, preside over liturgical prayers, confer baptism and distribute Holy Communion, in accordance with the provisions of the law.
Take care
Dennis