Q: May the priest omit the homily on Fridays?
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A: GIRM 66 says, “On Sundays and Holydays of Obligation there is to be a Homily at every Mass that is celebrated with the people attending and it may not be omitted without a grave reason. On other days it is recommended, especially on the weekdays of Advent, Lent and Easter Time, as well as on other festive days and occasions when the people come to church in greater numbers.”
So, yes, a homily may be omitted on any weekday, but it is recommended. I preach every day.