Pretty lightweight — it SSHes into each box and runs homebutler locally there, so the overhead is basically one SSH connection + a quick read of /proc and the Docker socket per check. No background daemon sitting there polling, it only runs when you ask or when alerts --watch fires.
I run it across 3 machines (Mac Mini, Pi 5, and another box) and haven't noticed any impact. The binary itself is ~15MB and idles at zero CPU since it's not a long-running service.