Term also applies to breasts with larger/longer nipples. The idea is that hanging sinker weights over long periods of time will stretch them and make them longer and possibly more sensitive.
The bane of musicians all over the world: a music stand that sinks by itself, caused by stripped threading inside the bore of the stand.
John, get yourself another music stand. This one's a sinker. The conductor'll keep on badmouthing you 'cause you'll wind up staring down at the music and not at him!