A method and system for controlling broadcast of system messaging from a relay, where the relay provides service on a first air interface and is configured to periodically broadcast on the first air interface a system message useable by WCDs to facilitate acquisition of wireless connectivity with the relay, and where the relay is served by a donor base station over a second air interface on which the donor base station provides service. Per the disclosure, an entity detects that resource utilization on the second air interface on which the donor base station provides service is threshold high, and in response to at least that detecting, the relay is made to temporarily discontinue the periodic broadcast of the system message on the first air interface so as to prevent the acquisition of connectivity with the relay.