At my church weekly but at alternating services. On Sunday mornings there’s an early service and a late service. One has communion on the first, third, and fifth Sundays of the month, and the other on the second and fourth.
Many younger pastors are keen to offer Holy Communion weekly. Their older elder boards are often keen to maintain a schedule of every other week or 1st Sunday of the month.
The every week but at a different service fad would annoy me, both as a called and ordained minister and as a layman.